Related papers: A Higher Order Godunov Method for Radiation Hydrod…
From a mathematical perspective, radiation hydrodynamics can be thought of as a system of hyperbolic balance laws with dual multiscale behavior (multiscale behavior associated with the hyperbolic wave speeds as well as multiscale behavior…
Hyperbolic conservation laws with stiff source terms appear in the study of a variety of physical systems. Early work showed that the use of formally second-order accurate semi-implicit methods could lead to a substantial loss of accuracy,…
This paper presents a hybrid Godunov method for three-dimensional radiation hydrodynamics. The multidimensional technique outlined in this paper is an extension of the one-dimensional method that was developed by Sekora & Stone 2009, 2010.…
We describe a numerical algorithm to integrate the equations of radiation magnetohydrodynamics in multidimensions using Godunov methods. This algorithm solves the radiation moment equations in the mixed frame, without invoking any…
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…
We investigate the Riemann problem for the shallow water equations with variable and (possibly) discontinuous topography and provide a complete description of the properties of its solutions: existence; uniqueness in the non-resonant…
In this paper, a high-order gas-kinetic scheme is developed for the equation of radiation hydrodynamics in equilibrium-diffusion limit which describes the interaction between matter and radiation. To recover RHE, the Bhatnagar-Gross-Krook…
We present a second-order Godunov algorithm for multidimensional, ideal MHD. Our algorithm is based on the unsplit formulation of Colella (J. Comput. Phys. vol. 87, 1990), with all of the primary dependent variables centered at the same…
We present a new algorithm for solving ideal relativistic hydrodynamics based on Godunov method with an exact solution of Riemann problem for an arbitrary equation of state. Standard numerical tests are executed, such as the sound wave…
We describe a new Godunov algorithm for relativistic magnetohydrodynamics (RMHD) that combines a simple, unsplit second order accurate integrator with the constrained transport (CT) method for enforcing the solenoidal constraint on the…
We develop a new relativistic radiation hydrodynamics code based on the Monte-Carlo algorithm. In this code, we implement a new scheme to achieve the second-order accuracy in time in the limit of a large packet number for solving the…
In this paper, we present a high order finite difference solver for anisotropic diffusion problems based on the first-order hyperbolic system method. In particular, we demonstrate that the construction of a uniformly accurate fifth-order…
High-order Godunov methods for gas dynamics have become a standard tool for simulating different classes of astrophysical flows. Their accuracy is mostly determined by the spatial interpolant used to reconstruct the pair of Riemann states…
Godunov Smoothed Particle Hydrodynamics (Godunov SPH) method is a computational fluid dynamics method that utilizes a Riemann solver and achieves the second-order accuracy in space. In this paper, we extend the Godunov SPH method to elastic…
In this chapter, we aim at presenting the basic techniques necessary to go beyond the widely accepted paradigm of second-order numerics. We specifically focus on finite-volume schemes for hyperbolic conservation laws occuring in fluid…
We describe a module for the Athena code that solves the gray equations of radiation hydrodynamics (RHD), based on the first two moments of the radiative transfer equation. We use a combination of explicit Godunov methods to advance the gas…
We study the mathematical character of the angular moment equations of radiative transfer in spherical symmetry and conclude that the system is hyperbolic for general forms of the closure relation found in the literature. Hyperbolicity and…
Hydrodynamics is a powerful emergent theory for the large-scale behaviours in many-body systems, quantum or classical. It is a gradient series expansion, where different orders of spatial derivatives provide an effective description on…
A system of high-order adaptive multiresolution wavelet collocation upwind schemes are developed for the solution of hyperbolic conservation laws. A couple of asymmetrical wavelet bases with interpolation property are built to realize the…
We construct a solution to a $2\times 2$ strictly hyperbolic system of conservation laws, showing that the Godunov scheme \cite{Godunov59} can produce an arbitrarily large amount of oscillations. This happens when the speed of a shock is…