相关论文: A physical-constraints-preserving genuinely multid…
Simulating general relativistic hydrodynamics (GRHD) presents challenges such as handling curved spacetime, achieving high-order shock-capturing accuracy, and preserving key physical constraints (positive density, pressure, and subluminal…
We assess the suitability of a recent high-resolution central scheme developed by Kurganov & Tadmor (2000) for the solution of the relativistic hydrodynamics equations. The novelty of this approach relies on the absence of Riemann solvers…
The current status of numerical solutions for the equations of ideal general relativistic hydrodynamics is reviewed. With respect to an earlier version of the article the present update provides additional information on numerical schemes…
This paper describes a multidimensional hydrodynamic code which can be used for studies of relativistic astrophysical flows. The code solves the special relativistic hydrodynamic equations as a hyperbolic system of conservation laws based…
High-order reconstruction schemes for the solution of hyperbolic conservation laws in orthogonal curvilinear coordinates are revised in the finite volume approach. The formulation employs a piecewise polynomial approximation to the…
The fluid flow transport and hydrodynamic problems often take the form of hyperbolic systems of conservation laws. In this work we will present a new scheme of finite volume methods for solving these evolution equations. It is a family of…
We present a general and practical procedure to solve the general relativistic hydrodynamic equations by using any of the special relativistic Riemann solvers recently developed for describing the evolution of special relativistic flows.…
In this paper we propose a novel thermodynamically compatible finite volume scheme for the numerical solution of the equations of magnetohydrodynamics (MHD) in one and two space dimensions. As shown by Godunov in 1972, the MHD system can be…
In this work we introduce a novel semi-implicit structure-preserving finite-volume/finite-difference scheme for the viscous and resistive equations of magnetohydrodynamics (MHD) based on an appropriate 3-split of the governing PDE system,…
The shallow water equations are numerically solved to simulate free surface flows. The convective flux terms in the shallow water equations need to be discretized using a Riemann solver to capture shocks and discontinuity for certain flow…
The ideal gas equation of state (EOS) with a constant adiabatic index is a poor approximation for most relativistic astrophysical flows, although it is commonly used in relativistic hydrodynamics. The paper develops high-order accurate…
We present a new high-order finite volume reconstruction method for hyperbolic conservation laws. The method is based on a piecewise cubic polynomial which provides its solutions a fifth-order accuracy in space. The spatially reconstructed…
We present a finite-volume, genuinely 4th-order accurate numerical method for solving the equations of resistive relativistic magnetohydrodynamics (Res-RMHD) in Cartesian coordinates. In our formulation, the magnetic field is evolved in…
In this paper, we present an approach to solving the Riemann problem in one-dimensional relativistic hydrodynamics, where the most computationally expensive steps of the exact solver are replaced by compact, highly specialized neural…
This paper presents a novel high-order cell-centered Lagrangian scheme for 2D compressible hydrodynamics by bridging the multi-moment constrained finite volume method (MCV) [16, 51, 52] with a nodal Riemann solver. This scheme (denoted by…
After we derive the Serre system of equations of water wave theory from a generalized variational principle, we present some of its structural properties. We also propose a robust and accurate finite volume scheme to solve these equations…
In this work, we introduce a framework to design multidimensional Riemann solvers for nonlinear systems of hyperbolic conservation laws on general unstructured polygonal Voronoi-like tessellations. In this framework we propose two simple…
We present a well-balanced finite volume solver for the compressible Euler equations with gravity where the approximate Riemann solver is derived using a relaxation approach. Besides the well-balanced property, the scheme is robust with…
It is known that HLL-type schemes are more dissipative than schemes based on characteristic decompositions. However, HLL-type methods offer greater flexibility to large systems of hyperbolic conservation laws because the eigenstructure of…
An implicit algorithm for solving the equations of general relativistic hydrodynamics in conservative form in three-dimensional axi-symmetry is presented. This algorithm is a direct extension of the pseudo-Newtonian implicit radiative…