本文基于MUSCL-Hancock数据重构方法提出了一种求解相对论流体力学方程的高分辨率熵相容格式(EC-MHM格式)。首先将一个修正的斜率限制器应用到MUSCL-Hancock方法的数据重构中,使之与熵相容格式结合,从而得到高分辨率的熵相容通量;在时间...本文基于MUSCL-Hancock数据重构方法提出了一种求解相对论流体力学方程的高分辨率熵相容格式(EC-MHM格式)。首先将一个修正的斜率限制器应用到MUSCL-Hancock方法的数据重构中,使之与熵相容格式结合,从而得到高分辨率的熵相容通量;在时间上,主要利用双曲守恒律方程的守恒型差分形式来更新下一时间层,从而提高了格式的计算效率。文中还证明了熵相容格式的收敛性。新格式在解的光滑区域具有高精度的特性,然而在间断区域,EC-MHM格式可以有效抑制非物理现象的发生;最后通过一系列数值算例验证了新格式具有无振荡、高分辨率等良好性能。This paper presents a high-resolution entropy-consistent scheme, termed the EC-MHM (Entropy-consistent, MUSCL-type High-resolution Method), for solving relativistic hydrodynamics equations, based on the MUSCL-Hancock data reconstruction methodology. Firstly, a modified slope limiter is applied to the data reconstruction of MUSCL-Hancock method, and combine it with the entropy consistent scheme, so as to obtain the high resolution entropy consistent flux. For the discretization of time derivative, the conservative finite difference scheme of hyperbolic conservation laws is adopted to update the solution at the next time level. The convergence of the entropy consistent scheme is also proved. In regions where the solution is smooth, the EC-MHM scheme exhibits high precision characteristics. Conversely, in discontinuous zones, the EC-MHM can effectively prevent the occurrence of non-physical phenomena. Finally, a series of numerical examples are simulated, and the new scheme is proved to have good properties such as no oscillation and high resolution.展开更多
A two-dimensional （2D） dam-break flow numerical model was developed based on the finite-volume total variation diminishing （TVD） and monotone upstream-centered scheme for conservation laws （MUSCL）-Hancock scheme...A two-dimensional （2D） dam-break flow numerical model was developed based on the finite-volume total variation diminishing （TVD） and monotone upstream-centered scheme for conservation laws （MUSCL）-Hancock scheme, which has second-order accuracy in both time and space. A Harten-Lax-van Leer-contact （HLLC） approximate Riemann solver was used to evaluate fluxes. The TVD MUSCL-Hancock numerical scheme utilizes slope limiters, such as the minmod, double minmod, superbee, van Albada, and van Leer limiters, to prevent spurious oscillations and maintain monotonicity near discontinuities. A comparative study of the impact of various slope limiters on the accuracy of the numerical flow model was conducted with several dam-break examples including wet and dry bed cases. The numerical results of the superbee and double minmod limiters agree better with the theoretical solution and have higher accuracy than other limiters in one-dimensional （1D） space. The ratio of the downstream water depth to the upstream water depth was used to select the proper slope limiter. For the 2D numerical model, the superbee limiter should not be used, owing to significant numerical dispersion.展开更多
In this study,a stable and robust interface-capturing method is developed to resolve inviscid,compressible two-fluid flows with general equation of state(EOS).The governing equations consist of mass conservation equat...In this study,a stable and robust interface-capturing method is developed to resolve inviscid,compressible two-fluid flows with general equation of state(EOS).The governing equations consist of mass conservation equation for each fluid,momentum and energy equations for mixture and an advection equation for volume fraction of one fluid component.Assumption of pressure equilibrium across an interface is used to close the model system.MUSCL-Hancock scheme is extended to construct input states for Riemann problems,whose solutions are calculated using generalized HLLC approximate Riemann solver.Adaptive mesh refinement(AMR)capability is built into hydrodynamic code.The resulting method has some advantages.First,it is very stable and robust,as the advection equation is handled properly.Second,general equation of state can model more materials than simple EOSs such as ideal and stiffened gas EOSs for example.In addition,AMR enables us to properly resolve flow features at disparate scales.Finally,this method is quite simple,time-efficient and easy to implement.展开更多
文摘本文基于MUSCL-Hancock数据重构方法提出了一种求解相对论流体力学方程的高分辨率熵相容格式(EC-MHM格式)。首先将一个修正的斜率限制器应用到MUSCL-Hancock方法的数据重构中,使之与熵相容格式结合,从而得到高分辨率的熵相容通量;在时间上,主要利用双曲守恒律方程的守恒型差分形式来更新下一时间层,从而提高了格式的计算效率。文中还证明了熵相容格式的收敛性。新格式在解的光滑区域具有高精度的特性,然而在间断区域,EC-MHM格式可以有效抑制非物理现象的发生;最后通过一系列数值算例验证了新格式具有无振荡、高分辨率等良好性能。This paper presents a high-resolution entropy-consistent scheme, termed the EC-MHM (Entropy-consistent, MUSCL-type High-resolution Method), for solving relativistic hydrodynamics equations, based on the MUSCL-Hancock data reconstruction methodology. Firstly, a modified slope limiter is applied to the data reconstruction of MUSCL-Hancock method, and combine it with the entropy consistent scheme, so as to obtain the high resolution entropy consistent flux. For the discretization of time derivative, the conservative finite difference scheme of hyperbolic conservation laws is adopted to update the solution at the next time level. The convergence of the entropy consistent scheme is also proved. In regions where the solution is smooth, the EC-MHM scheme exhibits high precision characteristics. Conversely, in discontinuous zones, the EC-MHM can effectively prevent the occurrence of non-physical phenomena. Finally, a series of numerical examples are simulated, and the new scheme is proved to have good properties such as no oscillation and high resolution.
基金supported by the National Natural Science Foundation of China(Grants No.51679170,51379157,and 51439007)
文摘A two-dimensional （2D） dam-break flow numerical model was developed based on the finite-volume total variation diminishing （TVD） and monotone upstream-centered scheme for conservation laws （MUSCL）-Hancock scheme, which has second-order accuracy in both time and space. A Harten-Lax-van Leer-contact （HLLC） approximate Riemann solver was used to evaluate fluxes. The TVD MUSCL-Hancock numerical scheme utilizes slope limiters, such as the minmod, double minmod, superbee, van Albada, and van Leer limiters, to prevent spurious oscillations and maintain monotonicity near discontinuities. A comparative study of the impact of various slope limiters on the accuracy of the numerical flow model was conducted with several dam-break examples including wet and dry bed cases. The numerical results of the superbee and double minmod limiters agree better with the theoretical solution and have higher accuracy than other limiters in one-dimensional （1D） space. The ratio of the downstream water depth to the upstream water depth was used to select the proper slope limiter. For the 2D numerical model, the superbee limiter should not be used, owing to significant numerical dispersion.
文摘In this study,a stable and robust interface-capturing method is developed to resolve inviscid,compressible two-fluid flows with general equation of state(EOS).The governing equations consist of mass conservation equation for each fluid,momentum and energy equations for mixture and an advection equation for volume fraction of one fluid component.Assumption of pressure equilibrium across an interface is used to close the model system.MUSCL-Hancock scheme is extended to construct input states for Riemann problems,whose solutions are calculated using generalized HLLC approximate Riemann solver.Adaptive mesh refinement(AMR)capability is built into hydrodynamic code.The resulting method has some advantages.First,it is very stable and robust,as the advection equation is handled properly.Second,general equation of state can model more materials than simple EOSs such as ideal and stiffened gas EOSs for example.In addition,AMR enables us to properly resolve flow features at disparate scales.Finally,this method is quite simple,time-efficient and easy to implement.
