Related papers: Non-Oscillatory Central Difference and Artificial …
Simple modifications for higher-order Godunov-type difference schemes are presented which allow for accurate advection of multi-fluid flows in hydrodynamic simulations. The constraint that the sum of all mass fractions has to be equal to…
We present a numerical method to solve the equations of general relativistic hydrodynamics in a given external gravitational field. The method is based on a generalization of Roe's approximate Riemann solver for the non relativistic Euler…
In the physically non viscous fluid dynamics, "shock capturing" methods adopt either an artificial viscosity contribution or an appropriate Riemann solver algorithm. These techniques are necessary to solve the strictly hyperbolic Euler…
We present a new numerical method of special relativistic resistive magnetohydrodynamics with scalar resistivity that can treat a range of phenomena, from nonrelativistic to relativistic (shock, contact discontinuity, and Alfv\'en wave).…
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.…
Discontinuous Galerkin (DG) methods coupled to WENO algorithms allow high order convergence for smooth problems and for the simulation of discontinuities and shocks. In this work, we investigate WENO-DG algorithms in the context of…
An alternative first step approximation based on subgrid artificial viscosity modeling (SAV) is proposed for defect-deferred correction method (DDC) for incompresible Navier-Stokes equation at high Reynolds number. This new approach not…
In physically inviscid fluid dynamics, "shock capturing" methods adopt either an artificial viscosity contribution or an appropriate Riemann solver algorithm. These techniques are necessary to solve the strictly hyperbolic Euler equations…
This is the first in a series of papers on the construction and validation of a three-dimensional code for general relativistic hydrodynamics, and its application to general relativistic astrophysics. This paper studies the consistency and…
In this work, we introduce a novel approach to formulating an artificial viscosity for shock capturing in nonlinear hyperbolic systems by utilizing the property that the solutions of hyperbolic conservation laws are not reversible in time…
We conduct a numerical study of relativistic viscous fluid dynamics in the Density Frame for one-dimensional fluid flows. The Density Frame is a formulation of relativistic viscous hydrodynamics that is first-order in time, requires no…
This is the second part to our companion paper [18]. Herein, we generalize to two space dimensions the C-method developed in [20,18] for adding localized, space-time smooth artificial viscosity to nonlinear systems of conservation laws that…
We develop a numerical hydrodynamics code using a pseudo-Newtonian formulation that uses the weak field approximation for the geometry, and a generalized source term for the Poisson equation that takes into account relativistic effects. The…
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…
Variable density incompressible flows are governed by parabolic equations. The artificial compressibility method makes these equations hyperbolic-type, which means that they can be solved using techniques developed for compressible flows,…
Numerical simulation of viscoelastic flows is challenging because of the hyperbolic nature of viscoelastic constitutive equations. Despite their superior accuracy and efficiency, pseudo-spectral methods require the introduction of…
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 article provides a computational evaluation of the popular high resolution upwind WACEB, CUBISTA and ADBQUICKEST schemes for solving non-linear fluid dynamics problems. By using the finite difference methodology, the schemes are…
We present a new hydrodynamic scheme named Godunov Density-Independent Smoothed Particle Hydrodynamics (GDISPH), that can accurately handle shock waves and contact discontinuities without any manually tuned parameters. This is in contrast…
We introduce a new methodology for adding localized, space-time smooth, artificial viscosity to nonlinear systems of conservation laws which propagate shock waves, rarefactions, and contact discontinuities, which we call the $C$-method. We…