High resolution, non-oscillatory, central difference (NOCD) numerical schemes are introduced as alternatives to more traditional artificial viscosity (AV) and Godunov methods for solving the fully general relativistic hydrody-namics equations. These new approaches provide the advantages of Godunov methods in capturing ultra-relativistic flows without the cost and complication of Riemann solvers...

The aim of this paper is to present a novel monotone upstream scheme for conservation law (MUSCL) on unstructured grids. The novel edge-based MUSCL scheme is devised to construct the required values at the midpoint of cell edges in a more straightforward and effective way compared to other conventional approaches, by making better use of the geometrical property of the triangular grids. The sch...

A particular case of initial data for the two-dimensional Euler equations is studied numerically. The results show that the Godunov method does not always converge to the physical solution, at least not on feasible grids. Moreover, they suggest that entropy solutions (in the weak entropy inequality sense) are not unique.

A third-order accurate Godunov-type scheme for the approximate solution of hyperbolic systems of conservation laws is presented. Its two main ingredients include: 1. A non-oscillatory piecewise-quadratic reconstruction of pointvalues from their given cell averages; and 2. A central differencing based on staggered evolution of the reconstructed cell averages. This results in a third-order centra...

This paper presents a new computational framework for the simulation of solid mechanics on general overlapping grids with adaptive mesh refinement (AMR). The approach, described here for time-dependent linear elasticity in two and three space dimensions, is motivated by considerations of accuracy, efficiency and flexibility. We consider two approaches for the numerical solution of the equations...

Currently, the Discontinuous Galerkin Method (DGM) is widely used to solve complex multi-scale problems of mathematical physics that have important applied significance. When implementing it, question choosing a discrete approximation flows for viscous terms Navier-Stokes equation important. It necessary focus on construction limiting functions, selection best approximations diffusion flows, an...

Classical finite volume schemes for the Euler system are not accurate at low Mach number and some fixes have to be used were developed in a vast literature over last two decades. The question we interested this article is: What about if porosity is no longer uniform? We first show that problem may understood on linear wave equation taking into account porosity. explain influence of cell geometr...

A new method is developed to approximate a first-order Hamilton–Jacobi equation. The constant motion of an interface in the normal direction interest. captured with help “Level-Set” function approximated through finite-volume Godunov-type scheme. Contrarily most computational approaches that consider smooth Level-Set functions, present one considers sharp “Level-Set”, numerical diffusion being ...

The solution of hyperbolic systems with sti source terms is of great importance in areas such as atmospheric dispersion. The nite-volume approach used here for such problems employs Godunov-type methods, a sophisticated splitting approach for e ciency and adaptive tetrahedral meshes to provide the necessary resolution for physically meaningful solutions. This raises the issues of how to estimat...