相关论文: ECHO: an Eulerian Conservative High Order scheme f…

The present work concerns the derivation of a numerical scheme to approximate weak solutions of the Euler equations with a gravitational source term. The designed scheme is proved to be fully well-balanced since it is able to exactly…

In this paper, we first propose a filter-based continuous Ensemble Eddy Viscosity (EEV) model for stochastic turbulent flow problems. We then propose a generic algorithm for a family of fully discrete, grad-div regularized, efficient…

In this article, we provide notes that complement the lectures on the relativistic Euler equations and shocks that were given by the second author at the program Mathematical Perspectives of Gravitation Beyond the Vacuum Regime, which was…

A new second-order method for approximating the compressible Euler equations is introduced. The method preserves all the known invariant domains of the Euler system: positivity of the density, positivity of the internal energy and the local…

The Einstein and Maxwell equations are both systems of hyperbolic equations which need to satisfy a set of elliptic constraints throughout evolution. However, while electrodynamics (EM) and magnetohydrodynamics (MHD) have benefited from a…

In this paper we present a novel approach for the design of high order general boundary conditions when approximating solutions of the Euler equations on domains with curved boundaries, using meshes which may not be boundary conformal. When…

Higher order finite volume schemes for magnetohydrodynamics (MHD) and relativistic magnetohydrodynamics (RMHD) are very valuable because they allow us to carry out astrophysical simulations with very high accuracy. However, astrophysical…

Numerical simulations of multidimensional astrophysical fluids present considerable challenges. However, the development of exascale computing has significantly enhanced computational capabilities, motivating the development of new codes…

This paper develops the high-order accurate entropy stable finite difference schemes for one- and two-dimensional special relativistic hydrodynamic equations. The schemes are built on the entropy conservative flux and the weighted…

This paper presents applications of weighted meshless scheme for conservation laws to the Euler equations and the equations of ideal magnetohydrodynamics. The divergence constraint of the latter is maintained to the truncation error by a…

We introduce a novel structure-preserving method in order to approximate the compressible ideal Magnetohydrodynamics (MHD) equations. This technique addresses the MHD equations using a non-divergence formulation, where the contributions of…

In this work, we develop a new hydrostatic reconstruction procedure to construct well-balanced schemes for one and multilayer shallow water flows, including wetting and drying. Initially, we derive the method for a path-conservative finite…

In this article we present a new family of high order accurate Arbitrary Lagrangian-Eulerian one-step WENO finite volume schemes for the solution of stiff hyperbolic balance laws. High order accuracy in space is obtained with a standard…

In this work, we present a positivity-preserving adaptive filtering approach for discontinuous spectral element approximations of the ideal magnetohydrodynamics equations. This approach combines the entropy filtering method (Dzanic and…

This paper presents an extension of the hybrid scheme proposed by Wang et al. (J. Comput. Phys. 229 (2010) 169-180) for numerical simulation of compressible isotropic turbulence to flows with higher turbulent Mach numbers. The scheme still…

This paper presents a novel structure-preserving scheme for Euler equations, focusing on the numerical conservation of entropy and kinetic energy. Explicit flux functions engineered to conserve entropy are introduced within the…

The weighted essentially non-oscillatory (WENO) methods are popular and effective spatial discretization methods for nonlinear hyperbolic partial differential equations. Although these methods are formally first-order accurate when a shock…

We assess the validity of a single step Godunov scheme for the solution of the magneto-hydrodynamics equations in more than one dimension. The scheme is second-order accurate and the temporal discretization is based on the dimensionally…

In this paper, we utilize the maximum-principle-preserving flux limiting technique, originally designed for high order weighted essentially non-oscillatory (WENO) methods for scalar hyperbolic conservation laws, to develop a class of high…

We present a novel method of magnetohydrodynamics (MHD) within the smoothed particle hydrodynamics scheme using the Geometric Density average force expression (GDSPH). GDSPH has recently been shown to reduce the leading order errors and…