The rotational incremental pressure-correction(RIPC)scheme,described in Timmermans et al.[Int.J.Numer.Methods.Fluids.,22(1996)]and Shen et al.[Math.Comput.,73(2003)]for non-rotational Navier-Stokes equations,is extend...The rotational incremental pressure-correction(RIPC)scheme,described in Timmermans et al.[Int.J.Numer.Methods.Fluids.,22(1996)]and Shen et al.[Math.Comput.,73(2003)]for non-rotational Navier-Stokes equations,is extended to rotating incompressible flows.The method is implemented in the context of a pseudo Fourier-spectral code and applied to several rotating laminar and turbulent flows.The performance of the scheme and the computational results are compared to the socalled diagonalization method(DM)developed by Morinishi et al.[Int.J.Heat.Fluid.Flow.,22(2001)].The RIPC predictions are in excellent agreement with the DM predictions,while being simpler to implement and computationally more efficient.The RIPC scheme is not in anyway limited to implementation in a pseudo-spectral code or periodic boundary conditions,and can be used in complex geometries and with other suitable boundary conditions.展开更多
In this paper,we construct two fully decoupled,second-order semi-discrete numerical schemes for the Boussinesq equations based on the scalar auxiliary variable(SAV)approach.By introducing a scalar auxiliary variable,t...In this paper,we construct two fully decoupled,second-order semi-discrete numerical schemes for the Boussinesq equations based on the scalar auxiliary variable(SAV)approach.By introducing a scalar auxiliary variable,the original Boussinesq system is transformed into an equivalent one.Then we discretize it using the second-order backward di erentiation formula(BDF2)and Crank-Nicolson(CN)to obtain two second-order time-advanced schemes.In both numerical schemes,a pressure-correction method is employed to decouple the velocity and pressure.These two schemes possess the desired property that they can be fully decoupled with satisfying unconditional stability.We rigorously prove both the unconditional stability and unique solvability of the discrete schemes.Furthermore,we provide detailed implementations of the decoupling procedures.Finally,various 2D numerical simulations are performed to verify the accuracy and energy stability of the proposed schemes.展开更多
The geomagnetic storm is one of the most important geomagnetic disturbance phenomena in the geospace.Many studies assume that input of solar wind energy into the Earth's ring current only occurs when IMF Bz in GSM...The geomagnetic storm is one of the most important geomagnetic disturbance phenomena in the geospace.Many studies assume that input of solar wind energy into the Earth's ring current only occurs when IMF Bz in GSM coordinates is southward;the ring current energy injection and decay under northward IMF Bz are not well understood and still need further investigation.In this paper,by using the large amount of data from the year 1964 to 2010,we use the empirical phase space analysis method to study the ring current energy injection and decay under northward IMF Bz and compare the results with those under southward IMF Bz condition.We have found that the largest injection Q under northward IMF Bz condition is only 7% of the largest injection under southward IMF Bz,implying that there is a very limit energy injected into the ring current region when IMF Bz is northward.The decay time decreases as VBz increases and shows a good linear trend for southward IMF Bz;while for the northward IMF Bz,there is not a clear relation between τ varies and VBz.Having taken τ as a function of injection Q instead of VBz,we have obtained the empirical relation of τ with Q for northward and southward IMF Bz conditions:the two categories are further combined together and the empirical relation τ= e(2.6 0.039 Q) is derived.Further,the pressure-corrected Dst formula Dst=Dst b P+c is derived for both southward and northward IMF Bz conditions,where the coefficients b and c are 6.9/10.4 and 10.0/15.2 when IMF Bz is southward and northward respectively.The statistical results on between the different geomagnetic indices(Dst,Kp,AE) and IMF Bz are also obtained.展开更多
The paper presents a novel pressure-corrected formulation of the immersed boundary method(IBM)for the simulation of fully compressible non-Boussinesq natural convection flows.The formulation incorporated into the pres...The paper presents a novel pressure-corrected formulation of the immersed boundary method(IBM)for the simulation of fully compressible non-Boussinesq natural convection flows.The formulation incorporated into the pressure-based fractional step approach facilitates simulation of the flows in the presence of an immersed body characterized by a complex geometry.Here,we first present extensive grid independence and verification studies addressing incompressible pressure-driven flow in an extended channel and non-Boussinesq natural convection flow in a differentially heated cavity.Next,the steady-state non-Boussinesq natural convection flow developing in the presence of hot cylinders of various diameters placed within a cold square cavity is thoroughly investigated.The obtained results are presented and analyzed in terms of the spatial distribution of path lines and temperature fields and of heat flux values typical of the hot cylinder and the cold cavity surfaces.Flow characteristics of multiple steady-state solutions discovered for several configurations are presented and discussed in detail.展开更多
基金This work is partially supported by NSF grants CBET-0651788 and DMS-0915066.
文摘The rotational incremental pressure-correction(RIPC)scheme,described in Timmermans et al.[Int.J.Numer.Methods.Fluids.,22(1996)]and Shen et al.[Math.Comput.,73(2003)]for non-rotational Navier-Stokes equations,is extended to rotating incompressible flows.The method is implemented in the context of a pseudo Fourier-spectral code and applied to several rotating laminar and turbulent flows.The performance of the scheme and the computational results are compared to the socalled diagonalization method(DM)developed by Morinishi et al.[Int.J.Heat.Fluid.Flow.,22(2001)].The RIPC predictions are in excellent agreement with the DM predictions,while being simpler to implement and computationally more efficient.The RIPC scheme is not in anyway limited to implementation in a pseudo-spectral code or periodic boundary conditions,and can be used in complex geometries and with other suitable boundary conditions.
基金Supported by Research Project Supported by Shanxi Scholarship Council of China(2021-029)International Cooperation Base and Platform Project of Shanxi Province(202104041101019)+2 种基金Basic Research Plan of Shanxi Province(202203021211129)Shanxi Province Natural Science Research(202203021212249)Special/Youth Foundation of Taiyuan University of Technology(2022QN101)。
文摘In this paper,we construct two fully decoupled,second-order semi-discrete numerical schemes for the Boussinesq equations based on the scalar auxiliary variable(SAV)approach.By introducing a scalar auxiliary variable,the original Boussinesq system is transformed into an equivalent one.Then we discretize it using the second-order backward di erentiation formula(BDF2)and Crank-Nicolson(CN)to obtain two second-order time-advanced schemes.In both numerical schemes,a pressure-correction method is employed to decouple the velocity and pressure.These two schemes possess the desired property that they can be fully decoupled with satisfying unconditional stability.We rigorously prove both the unconditional stability and unique solvability of the discrete schemes.Furthermore,we provide detailed implementations of the decoupling procedures.Finally,various 2D numerical simulations are performed to verify the accuracy and energy stability of the proposed schemes.
文摘The geomagnetic storm is one of the most important geomagnetic disturbance phenomena in the geospace.Many studies assume that input of solar wind energy into the Earth's ring current only occurs when IMF Bz in GSM coordinates is southward;the ring current energy injection and decay under northward IMF Bz are not well understood and still need further investigation.In this paper,by using the large amount of data from the year 1964 to 2010,we use the empirical phase space analysis method to study the ring current energy injection and decay under northward IMF Bz and compare the results with those under southward IMF Bz condition.We have found that the largest injection Q under northward IMF Bz condition is only 7% of the largest injection under southward IMF Bz,implying that there is a very limit energy injected into the ring current region when IMF Bz is northward.The decay time decreases as VBz increases and shows a good linear trend for southward IMF Bz;while for the northward IMF Bz,there is not a clear relation between τ varies and VBz.Having taken τ as a function of injection Q instead of VBz,we have obtained the empirical relation of τ with Q for northward and southward IMF Bz conditions:the two categories are further combined together and the empirical relation τ= e(2.6 0.039 Q) is derived.Further,the pressure-corrected Dst formula Dst=Dst b P+c is derived for both southward and northward IMF Bz conditions,where the coefficients b and c are 6.9/10.4 and 10.0/15.2 when IMF Bz is southward and northward respectively.The statistical results on between the different geomagnetic indices(Dst,Kp,AE) and IMF Bz are also obtained.
基金financial support for this work(grant 218-11-038).
文摘The paper presents a novel pressure-corrected formulation of the immersed boundary method(IBM)for the simulation of fully compressible non-Boussinesq natural convection flows.The formulation incorporated into the pressure-based fractional step approach facilitates simulation of the flows in the presence of an immersed body characterized by a complex geometry.Here,we first present extensive grid independence and verification studies addressing incompressible pressure-driven flow in an extended channel and non-Boussinesq natural convection flow in a differentially heated cavity.Next,the steady-state non-Boussinesq natural convection flow developing in the presence of hot cylinders of various diameters placed within a cold square cavity is thoroughly investigated.The obtained results are presented and analyzed in terms of the spatial distribution of path lines and temperature fields and of heat flux values typical of the hot cylinder and the cold cavity surfaces.Flow characteristics of multiple steady-state solutions discovered for several configurations are presented and discussed in detail.
