相关论文: A high-order weighted finite difference scheme wit…
This paper proposes and analyzes a novel efficient high-order finite volume method for the ideal magnetohydrodynamics (MHD). As a distinctive feature, the method simultaneously preserves a discretely divergence-free (DDF) constraint on the…
The magnetohydrodynamics (MHD) equations are generally known to be difficult to solve numerically, due to their highly nonlinear structure and the strong coupling between the electromagnetic and hydrodynamic variables, especially for high…
A Finite Volume (FV) scheme is developed for solving the extended magnetohydrodynamic (XMHD) equations, yielding accurate results in the ideal, resistive, and Hall MHD limits. This is accomplished by first re-writing the XMHD equations such…
We present projection-based mixed finite element methods for the solution of the unsteady Brinkman equations for incompressible single-phase flow with fixed in space porous solid inclusions. At each time step the method requires the…
Context: Calculating stellar pulsations requires a sufficient accuracy to match the quality of the observations. Many current pulsation codes apply a second order finite-difference scheme, combined with Richardson extrapolation to reach…
We study experimental convergence rates of three shock-capturing schemes for hyperbolic systems of conservation laws: the second-order central-upwind (CU) scheme, the third-order Rusanov-Burstein-Mirin (RBM), and the fifth-order alternative…
Understanding event-by-event correlations and fluctuations is crucial for the comprehension of the dynamics of heavy ion collisions. Relativistic hydrodynamics is an elegant tool for modeling these phenomena; however, such simulations are…
In this paper, we consider numerical approximation of an electrically conductive ferrofluid model, which consists of Navier-Stokes equations, magnetization equation, and magnetic induction equation. To solve this highly coupled, nonlinear,…
In this paper we construct high order finite volume schemes on networks of hyperbolic conservation laws with coupling conditions involving ODEs. We consider two generalized Riemann solvers at the junction, one of Toro-Castro type and a…
Most high order computational fluid dynamics (CFD) methods for compressible flows are based on Riemann solver for the flux evaluation and Runge-Kutta (RK) time stepping technique for temporal accuracy. The main advantage of this kind of…
We propose a simple modification of standard WENO finite volume methods for Cartesian grids, which retains the full spatial order of accuracy of the one-dimensional discretization when applied to nonlinear multidimensional systems of…
In this work, we consider the error estimates of some splitting schemes for the charged-particle dynamics under a strong magnetic field. We first propose a novel energy-preserving splitting scheme with computational cost per step…
In this paper, we construct a robust adaptive central-upwind scheme on unstructured triangular grids for two-dimensional shallow water equations with variable density. The method is well-balanced, positivity-preserving, and oscillation-free…
This paper presents entropy symmetrization and high-order accurate entropy stable schemes for the relativistic magnetohydrodynamic (RMHD) equations. It is shown that the conservative RMHD equations are not symmetrizable and do not admit a…
Numerical methods for the Euler equations with a singular source are discussed in this paper. The stationary discontinuity induced by the singular source and its coupling with the convection of fluid presents challenges to numerical…
With the advance of supercomputers we can now afford simulations with very large ranges of scales. In astrophysical applications, e.g. simulating Solar, stellar and planetary atmospheres, interstellar medium, etc; physical quantities, like…
We develop a two-dimensional high-order numerical scheme that exactly preserves and captures the moving steady states of the shallow water equations with topography or Manning friction. The high-order accuracy relies on a suitable…
In this paper, a class of high-order compact finite difference Hermite scheme is presented for the simulation of double-diffusive convection. To maintain linear stability, the convective fluxes are split into positive and negative parts,…
We present an efficient second-order finite difference scheme for solving the 2D sine-Gordon equation, which can inherit the discrete energy conservation for the undamped model theoretically. Due to the semi-implicit treatment for the…
This article aims at developing a high order pressure-based solver for the solution of the 3D compressible Navier-Stokes system at all Mach numbers. We propose a cell-centered discretization of the governing equations that splits the fluxes…