Many rock avalanches were triggered by the Wenchuan earthquake on May 12, 2008 in southwest China. Protection galleries covered with a single soil layer are usually used to protect against rockfall. Since one-layer pr...Many rock avalanches were triggered by the Wenchuan earthquake on May 12, 2008 in southwest China. Protection galleries covered with a single soil layer are usually used to protect against rockfall. Since one-layer protection galleries do not have sufficient buffer capacity, a two-layered absorbing system has been designed. This study aims to find whether an expanded poly-styrol （EPS） cushion, which is used in the soil-covered protection galleries for shock absorption, could be positioned under dynamic loadings. The dynamic impacts of the two-layered absorbing system under the conditions of rock avalanches are numerically simulated through a 2D discrete dement method. By selecting reasonable parameters, a series of numerical experiments were conducted to find the best combination for the two- layered absorbing system. The values of the EPS layer area as a percentage of the total area were set as 0% （Sl）, 22~ （S2）, and 70% （$3）. 22~ of the area of the EPS layer was found to be a reasonable value, and experiments were conducted to find the best position of the EPS layer in the two-layered absorbing system. The numerical results yield useful conclusions regarding the interaction between the impacting avalanches and the two-layered absorbing system. The soil layer can absorb the shock energy effectively and S2 （0.4-m thick EPS cushion covered with soil layer） is the most efficient combination, which can reduce the impact force, compared with the other combinations.展开更多
The two-layer cold storage method (TLM) was f irst reported in 1988, consisting of a perfluorochemical (PFC) and initially Euro-Collins' solution, which was later replaced by University of Wisconsin solution (UW)....The two-layer cold storage method (TLM) was f irst reported in 1988, consisting of a perfluorochemical (PFC) and initially Euro-Collins' solution, which was later replaced by University of Wisconsin solution (UW). PFC is a biologically inert liquid and acts as an oxygen-supplying agent. A pancreas preserved using the TLM is oxygenated through the PFC and substrates are supplied by the UW solution. This allows the pancreas preserved using the TLM to generate adenosine triphosphate during storage, prolonging the preservation time. In a canine model, the TLM was shown to repair and resuscitate warm ischemically damaged pancreata during preservation, improve pancreas graft survival after transplantation, and also improve the islet yield after isolation. Clinical trials using the TLM in pancreas preservation before whole-pancreas transplantation and islet isolation have shown promising outcomes. We describe the role of the TLM in pancreas and islet transplantation.展开更多
The derivation of Green function in a two-layer fluid model has been treated in different ways. In a two-layer fluid with the upper layer having a free surface, there exist two modes of waves propagating due to the fr...The derivation of Green function in a two-layer fluid model has been treated in different ways. In a two-layer fluid with the upper layer having a free surface, there exist two modes of waves propagating due to the free surface and the interface. This paper is concerned with the derivation of Green functions in the three dimensional case of a stationary source oscillating. The source point is located either in the upper or lower part of a two-layer fluid of finite depth. The derivation is carried out by the method of singularities. This method has an advantage in that it involves representing the potential as a sum of singularities or multipoles placed within any structures being present. Furthermore, experience shows that the systems of equations resulted from using a singularity method possess excellent convergence characteristics and only a few equations are needed to obtain accurate numerical results. Validation is done by showing that the derived two-layer Green function can be reduced to that of a single layer of finite depth or that the upper Green function coincides with that of the lower, for each case. The effect of the density on the internal waves is demonstrated. Also, it is shown how the surface and internal wave amplitudes are compared for both the wave modes. The fluid in this case is considered to be inviscid and incompressible and the flow is irrotational.展开更多
Electromagnetic （EM） scattering from a stack of two rough interfaces separating a homogeneous medium with a perfectly electric conducting （PEC） object has been calculated through the method of moments for vertical...Electromagnetic （EM） scattering from a stack of two rough interfaces separating a homogeneous medium with a perfectly electric conducting （PEC） object has been calculated through the method of moments for vertical polarization. Theoretical formulations of EM scattering from multi-layered rough interfaces with a PEC object have been derived in detail and the total fields and their normal derivatives on the rough interfaces are solved. The two-layered model is a special case. In this work, a Gaussian rough surface was applied to simulate the rough interface. A cylinder was located above, between or below the two-layered rough interfaces. Through numerical simulations, the validity of this work is demonstrated by comparing it with existing scattering models, which are special cases that include a PEC object located above/below a single-layered rough interface and two-layered rough interfaces without an object. Subsequently, the influences of characteristic parameters, such as the relative permittivity of the medium, as well as the average height between the two rough surfaces, on the bistatic scattering coefficient are discussed.展开更多
A baroclinic typhoon model with a moving multi--nested grid is applied in marine environmental forecasts. This paper describes the numerical methods of the model including governing equations, finite differencing, spl...A baroclinic typhoon model with a moving multi--nested grid is applied in marine environmental forecasts. This paper describes the numerical methods of the model including governing equations, finite differencing, split scheme and time integration.展开更多
This paper offers a new method to solve the problem of software pipelininsr on nested loops. We first introduce our new software pipelininog method. Ruminate Method, which can optimize program with nested loops. We al...This paper offers a new method to solve the problem of software pipelininsr on nested loops. We first introduce our new software pipelininog method. Ruminate Method, which can optimize program with nested loops. We also outline an algorithm to realize it and introduce the hardware support we designed. The performance of Ruminate Method is analyzed at the end of this paper with the aid of our preliminary experimental result.展开更多
The problem of three-dimensional(3D) acoustic scattering in a complex medium has aroused considerable interest of researchers for many years. An ultrasonic scattered field calculating technique is proposed to study th...The problem of three-dimensional(3D) acoustic scattering in a complex medium has aroused considerable interest of researchers for many years. An ultrasonic scattered field calculating technique is proposed to study the scattering echo from strongly scattered materials in a two-layer medium in this work. Firstly, with the high frequency stationary phase method,the Green's function of two-layer fluid media is derived. And then based on the idea of integral equation discretization,the Green's function method is extended to two-layer fluid media to derive the scattering field expression of defects in a complex medium. With this method, the scattering field of 3D defect in a two-layer medium is calculated and the characteristics of received echoes are studied. The results show that this method is able to solve the scattering P wave field of 3D defect with arbitrary shape at any scattering intensity in two-layer media. Considering the circumstance of waterimmersion ultrasonic non-destructive test(NDT), the scattering sound field characteristics of different types of defects are analyzed by simulation, which will help to optimize the detection scheme and corresponding imaging method in practice so as to improve the detection quality.展开更多
The standard lattice Boltzmann method utilizes uniform grids to maintain a compact computational procedure. However, it is often less efficient to perform hydrodynamic and aerodynamic flow simulations when there is a ...The standard lattice Boltzmann method utilizes uniform grids to maintain a compact computational procedure. However, it is often less efficient to perform hydrodynamic and aerodynamic flow simulations when there is a need for high resolution. To resolve these difficulties, a multiple nested lattice Boltzmann method(MNLBM) was developed, which contains several overlapped layers with different resolutions in the computational domain. The data transference of flow field on two layers is accomplished by a Filippova procedure which is proved to satisfy the continuity of mass, momentum, and stresses across the interface. The proposed method is based on the standard lattice Boltzmann method, so it is easily performed.By numerical investigation, the result of present method has been agreed with that of literature, but the computation efficiency is higher than the standard lattice Boltzmann method.展开更多
This paper is devoted to the analysis of the two-layer shallow-water equations representing gravity currents. A similarity technique which is the characteristic function method is applied for this study. The applicati...This paper is devoted to the analysis of the two-layer shallow-water equations representing gravity currents. A similarity technique which is the characteristic function method is applied for this study. The application of the characteristic function method makes it possible to obtain the similarity forms depending on a group of infinitesimal transformations. Thus, the number of independent variables is reduced by one and the governing partial differential equations with the auxiliary conditions reduce to a system of ordinary differential equations with the appropriate auxiliary conditions. Numeric solutions are presented and discussed.展开更多
In this study, the method of lines (MOLs) with higher order central difference approximation method coupled with the classical fourth order Runge-Kutta (RK(4,4)) method is used in solving shallow water equations (SWEs...In this study, the method of lines (MOLs) with higher order central difference approximation method coupled with the classical fourth order Runge-Kutta (RK(4,4)) method is used in solving shallow water equations (SWEs) in Cartesian coordinates to foresee water levels associated with a storm accurately along the coast of Bangladesh. In doing so, the partial derivatives of the SWEs with respect to the space variables were discretized with 5-point central difference, as a test case, to obtain a system of ordinary differential equations with time as an independent variable for every spatial grid point, which with initial conditions were solved by the RK(4,4) method. The complex land-sea interface and bottom topographic details were incorporated closely using nested schemes. The coastal and island boundaries were rectangularized through proper stair step representation, and the storing positions of the scalar and momentum variables were specified according to the rules of structured C-grid. A stable tidal regime was made over the model domain considering the effect of the major tidal constituent, M2 along the southern open boundary of the outermost parent scheme. The Meghna River fresh water discharge was taken into account for the inner most child scheme. To take into account the dynamic interaction of tide and surge, the generated tidal regime was introduced as the initial state of the sea, and the surge was then made to come over it through computer simulation. Numerical experiments were performed with the cyclone April 1991 to simulate water levels due to tide, surge, and their interaction at different stations along the coast of Bangladesh. Our computed results were found to compare reasonable well with the limited observed data obtained from Bangladesh Inland Water Transport Authority (BIWTA) and were found to be better in comparison with the results obtained through the regular finite difference method and the 3-point central difference MOLs coupled with the RK(4,4) method with regard to the root mean square error values.展开更多
A three-dimensional （3D） predictor-corrector finite difference method for standing wave is developed. It is applied to solve the 3D nonlinear potential flow equa- tions with a free surface. The 3D irregular tank is ...A three-dimensional （3D） predictor-corrector finite difference method for standing wave is developed. It is applied to solve the 3D nonlinear potential flow equa- tions with a free surface. The 3D irregular tank is mapped onto a fixed cubic tank through the proper coordinate transform schemes. The cubic tank is distributed by the staggered meshgrid, and the staggered meshgrid is used to denote the variables of the flow field. The predictor-corrector finite difference method is given to develop the difference equa- tions of the dynamic boundary equation and kinematic boundary equation. Experimental results show that, using the finite difference method of the predictor-corrector scheme, the numerical solutions agree well with the published results. The wave profiles of the standing wave with different amplitudes and wave lengths are studied. The numerical solutions are also analyzed and presented graphically.展开更多
The two-dimensional problems concerning the interaction of linear water waves with cylinders of arbitrary shape in two-layer deep water are investigated by use of the Boundary Integral Equation Method （BIEM）. Simple...The two-dimensional problems concerning the interaction of linear water waves with cylinders of arbitrary shape in two-layer deep water are investigated by use of the Boundary Integral Equation Method （BIEM）. Simpler new expressions for the Green functions are derived, and verified by comparison of results obtained by BIEM with those by an analytical method. Examined are the radiation and scattering of linear waves by two typical configurations of cylinders in two- layer deep water. Hydrodynamic behaviors including hydrodynamic coefficients, wave forces, reflection and transmission coef- ficients and energies are analyzed in detail, and some imeresting physical phenomena are observed.展开更多
The nested Bethe ansatz (BA) method is applied to find the eigenvalues and the eigenvectors of the transfer matrix for spin-ladder model with open boundary conditions. Based on the reflection equation, we find the gen...The nested Bethe ansatz (BA) method is applied to find the eigenvalues and the eigenvectors of the transfer matrix for spin-ladder model with open boundary conditions. Based on the reflection equation, we find the general diagonal solution, which determines the generalboundary interaction in the Hamiltonian. We introduce the spin-ladder model with open boundary conditions. By finding the solution K± of the reflection equation which determines the nontrivial boundary terms in the Hamiltonian, we diagonalize the transfer matrix of the spin-ladder model with open boundary conditions in the framework of nested BA.展开更多
A bearing capacity evaluation for the surface strip foundation on a working platform modelled on a twolayered substrate is considered in the study.The upper layer is assumed as man-made and wellcontrolled and thus non...A bearing capacity evaluation for the surface strip foundation on a working platform modelled on a twolayered substrate is considered in the study.The upper layer is assumed as man-made and wellcontrolled and thus non-variable.The lower layer modelling natural cohesive soil is subjected to spatial variability of undrained shear strength.The random failure mechanism method(RFMM)is used to evaluate the bearing capacity.This approach employs a kinematic assessment of the critical load and incorporates the averaging of three-dimensional(3 D)random field along dissipation surfaces that result from the failure mechanism geometry.A novel version of the approach considering an additional linear trend of undrained shear strength in the spatially variable layer is proposed.The high efficiency of the RFMM algorithm is preserved.The influences of foundation length,trend slope in the spatially variable layer,fluctuation scales,and thickness of the homogenous sand layer on the resulting bearing capacity evaluations are analysed.Moreover,for selected cases,verification of the RFMM based assessment obtained using random finite difference method(RFDM)based on 3 D analysis is provided.Two types of analyses are performed using RFDM based on associated and non-associated flow rules.For associated flow rule which corresponds to RFMM,the RFMM is conservative and efficient and thus it seems preferable.However,if RFDM employs non-associated flow rule(much lower dilation angle for sand layer),the efficient RFMM is no longer conservative.For this situation,a combined approach that improves the efficiency of the numerical method is suggested.展开更多
基金financial support from the Project of National Science Foundation of China(Grant No.41272346)the National Outstanding Youth Funds(Grant No.41225011)+2 种基金financial support from the Science & Technology Research Plan of China Railway Eryuan Engineering Group CO.LTD (Grant No.13164196(13-15))the Project of National Science Foundation of China(Grant Nos. 41472293,91430105)"hundred talents" program of CAS
文摘Many rock avalanches were triggered by the Wenchuan earthquake on May 12, 2008 in southwest China. Protection galleries covered with a single soil layer are usually used to protect against rockfall. Since one-layer protection galleries do not have sufficient buffer capacity, a two-layered absorbing system has been designed. This study aims to find whether an expanded poly-styrol （EPS） cushion, which is used in the soil-covered protection galleries for shock absorption, could be positioned under dynamic loadings. The dynamic impacts of the two-layered absorbing system under the conditions of rock avalanches are numerically simulated through a 2D discrete dement method. By selecting reasonable parameters, a series of numerical experiments were conducted to find the best combination for the two- layered absorbing system. The values of the EPS layer area as a percentage of the total area were set as 0% （Sl）, 22~ （S2）, and 70% （$3）. 22~ of the area of the EPS layer was found to be a reasonable value, and experiments were conducted to find the best position of the EPS layer in the two-layered absorbing system. The numerical results yield useful conclusions regarding the interaction between the impacting avalanches and the two-layered absorbing system. The soil layer can absorb the shock energy effectively and S2 （0.4-m thick EPS cushion covered with soil layer） is the most efficient combination, which can reduce the impact force, compared with the other combinations.
文摘The two-layer cold storage method (TLM) was f irst reported in 1988, consisting of a perfluorochemical (PFC) and initially Euro-Collins' solution, which was later replaced by University of Wisconsin solution (UW). PFC is a biologically inert liquid and acts as an oxygen-supplying agent. A pancreas preserved using the TLM is oxygenated through the PFC and substrates are supplied by the UW solution. This allows the pancreas preserved using the TLM to generate adenosine triphosphate during storage, prolonging the preservation time. In a canine model, the TLM was shown to repair and resuscitate warm ischemically damaged pancreata during preservation, improve pancreas graft survival after transplantation, and also improve the islet yield after isolation. Clinical trials using the TLM in pancreas preservation before whole-pancreas transplantation and islet isolation have shown promising outcomes. We describe the role of the TLM in pancreas and islet transplantation.
基金supported by the National Natural Science Foundation of China (Grant No. 50779008)
文摘The derivation of Green function in a two-layer fluid model has been treated in different ways. In a two-layer fluid with the upper layer having a free surface, there exist two modes of waves propagating due to the free surface and the interface. This paper is concerned with the derivation of Green functions in the three dimensional case of a stationary source oscillating. The source point is located either in the upper or lower part of a two-layer fluid of finite depth. The derivation is carried out by the method of singularities. This method has an advantage in that it involves representing the potential as a sum of singularities or multipoles placed within any structures being present. Furthermore, experience shows that the systems of equations resulted from using a singularity method possess excellent convergence characteristics and only a few equations are needed to obtain accurate numerical results. Validation is done by showing that the derived two-layer Green function can be reduced to that of a single layer of finite depth or that the upper Green function coincides with that of the lower, for each case. The effect of the density on the internal waves is demonstrated. Also, it is shown how the surface and internal wave amplitudes are compared for both the wave modes. The fluid in this case is considered to be inviscid and incompressible and the flow is irrotational.
基金Project supported by the National Natural Science Foundation of China (Grant No. 60971067)the Specialized Research Fund for the Doctoral Program of Higher Education,China (Grant No. 20100203110016)the Fundamental Research Funds for the Central Universities,China (Grant No. K50510070001)
文摘Electromagnetic （EM） scattering from a stack of two rough interfaces separating a homogeneous medium with a perfectly electric conducting （PEC） object has been calculated through the method of moments for vertical polarization. Theoretical formulations of EM scattering from multi-layered rough interfaces with a PEC object have been derived in detail and the total fields and their normal derivatives on the rough interfaces are solved. The two-layered model is a special case. In this work, a Gaussian rough surface was applied to simulate the rough interface. A cylinder was located above, between or below the two-layered rough interfaces. Through numerical simulations, the validity of this work is demonstrated by comparing it with existing scattering models, which are special cases that include a PEC object located above/below a single-layered rough interface and two-layered rough interfaces without an object. Subsequently, the influences of characteristic parameters, such as the relative permittivity of the medium, as well as the average height between the two rough surfaces, on the bistatic scattering coefficient are discussed.
基金supported by the Chinese National Research Program of Science and Technology under Project! 85-903-03-04.
文摘A baroclinic typhoon model with a moving multi--nested grid is applied in marine environmental forecasts. This paper describes the numerical methods of the model including governing equations, finite differencing, split scheme and time integration.
文摘This paper offers a new method to solve the problem of software pipelininsr on nested loops. We first introduce our new software pipelininog method. Ruminate Method, which can optimize program with nested loops. We also outline an algorithm to realize it and introduce the hardware support we designed. The performance of Ruminate Method is analyzed at the end of this paper with the aid of our preliminary experimental result.
基金Project supported by the Key Research Program of Frontier Sciences, Chinese Academy of Sciences (Grant No. ZDBS-LY-7023)。
文摘The problem of three-dimensional(3D) acoustic scattering in a complex medium has aroused considerable interest of researchers for many years. An ultrasonic scattered field calculating technique is proposed to study the scattering echo from strongly scattered materials in a two-layer medium in this work. Firstly, with the high frequency stationary phase method,the Green's function of two-layer fluid media is derived. And then based on the idea of integral equation discretization,the Green's function method is extended to two-layer fluid media to derive the scattering field expression of defects in a complex medium. With this method, the scattering field of 3D defect in a two-layer medium is calculated and the characteristics of received echoes are studied. The results show that this method is able to solve the scattering P wave field of 3D defect with arbitrary shape at any scattering intensity in two-layer media. Considering the circumstance of waterimmersion ultrasonic non-destructive test(NDT), the scattering sound field characteristics of different types of defects are analyzed by simulation, which will help to optimize the detection scheme and corresponding imaging method in practice so as to improve the detection quality.
文摘The standard lattice Boltzmann method utilizes uniform grids to maintain a compact computational procedure. However, it is often less efficient to perform hydrodynamic and aerodynamic flow simulations when there is a need for high resolution. To resolve these difficulties, a multiple nested lattice Boltzmann method(MNLBM) was developed, which contains several overlapped layers with different resolutions in the computational domain. The data transference of flow field on two layers is accomplished by a Filippova procedure which is proved to satisfy the continuity of mass, momentum, and stresses across the interface. The proposed method is based on the standard lattice Boltzmann method, so it is easily performed.By numerical investigation, the result of present method has been agreed with that of literature, but the computation efficiency is higher than the standard lattice Boltzmann method.
文摘This paper is devoted to the analysis of the two-layer shallow-water equations representing gravity currents. A similarity technique which is the characteristic function method is applied for this study. The application of the characteristic function method makes it possible to obtain the similarity forms depending on a group of infinitesimal transformations. Thus, the number of independent variables is reduced by one and the governing partial differential equations with the auxiliary conditions reduce to a system of ordinary differential equations with the appropriate auxiliary conditions. Numeric solutions are presented and discussed.
文摘In this study, the method of lines (MOLs) with higher order central difference approximation method coupled with the classical fourth order Runge-Kutta (RK(4,4)) method is used in solving shallow water equations (SWEs) in Cartesian coordinates to foresee water levels associated with a storm accurately along the coast of Bangladesh. In doing so, the partial derivatives of the SWEs with respect to the space variables were discretized with 5-point central difference, as a test case, to obtain a system of ordinary differential equations with time as an independent variable for every spatial grid point, which with initial conditions were solved by the RK(4,4) method. The complex land-sea interface and bottom topographic details were incorporated closely using nested schemes. The coastal and island boundaries were rectangularized through proper stair step representation, and the storing positions of the scalar and momentum variables were specified according to the rules of structured C-grid. A stable tidal regime was made over the model domain considering the effect of the major tidal constituent, M2 along the southern open boundary of the outermost parent scheme. The Meghna River fresh water discharge was taken into account for the inner most child scheme. To take into account the dynamic interaction of tide and surge, the generated tidal regime was introduced as the initial state of the sea, and the surge was then made to come over it through computer simulation. Numerical experiments were performed with the cyclone April 1991 to simulate water levels due to tide, surge, and their interaction at different stations along the coast of Bangladesh. Our computed results were found to compare reasonable well with the limited observed data obtained from Bangladesh Inland Water Transport Authority (BIWTA) and were found to be better in comparison with the results obtained through the regular finite difference method and the 3-point central difference MOLs coupled with the RK(4,4) method with regard to the root mean square error values.
基金supported by the Yunnan Provincial Applied Basic Research Program of China(No. KKSY201207019)
文摘A three-dimensional （3D） predictor-corrector finite difference method for standing wave is developed. It is applied to solve the 3D nonlinear potential flow equa- tions with a free surface. The 3D irregular tank is mapped onto a fixed cubic tank through the proper coordinate transform schemes. The cubic tank is distributed by the staggered meshgrid, and the staggered meshgrid is used to denote the variables of the flow field. The predictor-corrector finite difference method is given to develop the difference equa- tions of the dynamic boundary equation and kinematic boundary equation. Experimental results show that, using the finite difference method of the predictor-corrector scheme, the numerical solutions agree well with the published results. The wave profiles of the standing wave with different amplitudes and wave lengths are studied. The numerical solutions are also analyzed and presented graphically.
基金This work was financially supported bythe National Natural Science Foundation of China(Grant No50679078)
文摘The two-dimensional problems concerning the interaction of linear water waves with cylinders of arbitrary shape in two-layer deep water are investigated by use of the Boundary Integral Equation Method （BIEM）. Simpler new expressions for the Green functions are derived, and verified by comparison of results obtained by BIEM with those by an analytical method. Examined are the radiation and scattering of linear waves by two typical configurations of cylinders in two- layer deep water. Hydrodynamic behaviors including hydrodynamic coefficients, wave forces, reflection and transmission coef- ficients and energies are analyzed in detail, and some imeresting physical phenomena are observed.
文摘The nested Bethe ansatz (BA) method is applied to find the eigenvalues and the eigenvectors of the transfer matrix for spin-ladder model with open boundary conditions. Based on the reflection equation, we find the general diagonal solution, which determines the generalboundary interaction in the Hamiltonian. We introduce the spin-ladder model with open boundary conditions. By finding the solution K± of the reflection equation which determines the nontrivial boundary terms in the Hamiltonian, we diagonalize the transfer matrix of the spin-ladder model with open boundary conditions in the framework of nested BA.
文摘A bearing capacity evaluation for the surface strip foundation on a working platform modelled on a twolayered substrate is considered in the study.The upper layer is assumed as man-made and wellcontrolled and thus non-variable.The lower layer modelling natural cohesive soil is subjected to spatial variability of undrained shear strength.The random failure mechanism method(RFMM)is used to evaluate the bearing capacity.This approach employs a kinematic assessment of the critical load and incorporates the averaging of three-dimensional(3 D)random field along dissipation surfaces that result from the failure mechanism geometry.A novel version of the approach considering an additional linear trend of undrained shear strength in the spatially variable layer is proposed.The high efficiency of the RFMM algorithm is preserved.The influences of foundation length,trend slope in the spatially variable layer,fluctuation scales,and thickness of the homogenous sand layer on the resulting bearing capacity evaluations are analysed.Moreover,for selected cases,verification of the RFMM based assessment obtained using random finite difference method(RFDM)based on 3 D analysis is provided.Two types of analyses are performed using RFDM based on associated and non-associated flow rules.For associated flow rule which corresponds to RFMM,the RFMM is conservative and efficient and thus it seems preferable.However,if RFDM employs non-associated flow rule(much lower dilation angle for sand layer),the efficient RFMM is no longer conservative.For this situation,a combined approach that improves the efficiency of the numerical method is suggested.
