Related papers: A New Multidimensional Relativistic Hydrodynamics …
In this article, we propose a modified convex combination of the polynomial reconstructions of odd-order WENO schemes to maintain the central substencil prevalence over the lateral ones in all parts of the solution. New "centered" versions…
We propose an alternative reconstruction for weighted essentially non-oscillatory schemes with adaptive order (WENO-AO) for solving hyperbolic conservation laws. The alternative reconstruction has a more concise form than the original…
We propose novel less diffusive schemes for conservative one- and two-dimensional hyperbolic systems of nonlinear partial differential equations (PDEs). The main challenges in the development of accurate and robust numerical methods for the…
Higher order finite difference Weighted Essentially Non-Oscillatory (WENO) schemes for conservation laws represent a technology that has been reasonably consolidated. They are extremely popular because, when applied to multidimensional…
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,…
We study a conservative data-driven discretization for one-dimensional hyperbolic conservation laws based on the classical fifth-order WENO finite-volume scheme and a hypernetwork architecture. In the proposed Hyper--WENO5 Conservative-Form…
This paper presents a fully multidimensional kernel-based reconstruction scheme for finite volume methods applied to systems of hyperbolic conservation laws, with a particular emphasis on the compressible Euler equations. Non-oscillatory…
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…
Balsara (2001, J. Comput. Phys., 174, 614) showed the importance of divergence-free reconstruction in adaptive mesh refinement problems for magnetohydrodynamics (MHD) and the importance of the same for designing robust second order schemes…
Several relaxation approximations to partial differential equations have been recently proposed. Examples include conservation laws, Hamilton-Jacobi equations, convection-diffusion problems, gas dynamics problems. The present paper focuses…
We present a new high-resolution, non-oscillatory semi-discrete central-upwind scheme for one-dimensional two-layer shallow-water flows with friction and entrainment along channels with arbitrary cross sections and bottom topography. These…
A novel central weighted essentially non-oscillatory (central WENO; CWENO)-type scheme for the construction of high-resolution approximations to discontinuous solutions to hyperbolic systems of conservation laws is presented. This procedure…
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…
This review is concerned with a discussion of numerical methods for the solution of the equations of special relativistic hydrodynamics (SRHD). Particular emphasis is put on a comprehensive review of the application of high-resolution…
The paper describes a new upwind conservative numerical scheme for special relativistic resistive magnetohydrodynamics with scalar resistivity. The magnetic field is kept approximately divergence free and the divergence of the electric…
We propose a class of weighted compact central (WCC) schemes for solving hyperbolic conservation laws. The linear version can be considered as a high-order extension of the central Lax-Friedrichs (LxF) scheme and the central conservation…
In this paper we propose the first better than second order accurate method in space and time for the numerical solution of the resistive relativistic magnetohydrodynamics (RRMHD) equations on unstructured meshes in multiple space…
Many numerical schemes for hyperbolic systems require a piecewise polynomial reconstruction of the cell averaged values, and to simulate perturbed steady states accurately we require a so called 'well balanced' reconstruction scheme. For…
The present paper introduces a class of finite volume schemes of increasing order of accuracy in space and time for hyperbolic systems that are in conservation form. This paper specifically focuses on Euler system that is used for modeling…
Numerical schemes for the general relativistic hydrodynamic equations are discussed. The use of conservative algorithms based upon the characteristic structure of those equations, developed during the last decade building on ideas first…