Related papers: A "Neural" Riemann solver for Relativistic Hydrody…
Recently, designing neural solvers for large-scale linear systems of equations has emerged as a promising approach in scientific and engineering computing. This paper first introduce the Richardson(m) neural solver by employing a meta…
We describe a numerical method for calculating the (3+1) dimensional general relativistic hydrodynamics of a coalescing neutron-star binary system. The relativistic field equations are solved at each time slice with a spatial 3-metric…
Neural Networks (NNs) have been identified as a potentially powerful tool in the study of complex dynamical systems. A good example is the NN differential equation (DE) solver, which provides closed form, differentiable, functional…
A new approximate Riemann solver for the equations of magnetohydrodynamics (MHD) with an isothermal equation of state is presented. The proposed method of solution draws on the recent work of Miyoshi and Kusano, in the context of adiabatic…
The Generalized Riemann Problems (GRP) for nonlinear hyperbolic systems of balance laws in one space dimension are now well-known and can be formulated as follows: Given initial-data which are smooth on two sides of a discontinuity,…
The study of fluids has been a topic of intense research for several hundred years. Over the years, this has further increased due to improved computational facility, which makes it easy to numerically simulate the fluid dynamics, which was…
The importance of contact discontinuities in 2D isothermal flows has rarely been discussed, since most Riemann solvers are derived for 1D Euler equations. We present a new contact resolving approximate Riemann solver for the isothermal…
We propose a simple algebraic method for constructing exact solutions of equations of two-dimensional hydrodynamics of an incompressible fluid. The problem reduces to consecutively solving three linear partial differential equations for a…
Neural networks have shown great potential in accelerating the solution of partial differential equations (PDEs). Recently, there has been a growing interest in introducing physics constraints into training neural PDE solvers to reduce the…
In various astrophysics settings it is common to have a two-fluid relativistic plasma that interacts with the electromagnetic field. While it is common to ignore the displacement current in the ideal, classical magnetohydrodynamic limit,…
In this paper we analyze a 1+3 dimensional solution of relativistic hydrodynamics. We calculate momentum distribution and other observables from the solution and compare them to measurements from the Relativistic Heavy Ion Collider (RHIC).…
We present an adaptive multiresolution method for the numerical simulation of ideal magnetohydrodynamics in two space dimensions. The discretization uses a finite volume scheme based on a Cartesian mesh and an explicit compact Rung-Kutta…
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…
We investigate the numerical artifact known as a carbuncle, in the solution of the shallow water equations. We propose a new Riemann solver that is based on a local measure of the entropy residual and aims to avoid carbuncles while…
Residual distributions (RD) schemes are a class of of high-resolution finite volume methods for unstructured grids. A key feature of these schemes is that they make use of genuinely multidimensional (approximate) Riemann solvers as opposed…
In this paper, we develop a new method for magnetohydrodynamics (MHD) using smoothed particle hydrodynamics (SPH). To describe MHD shocks accurately, the Godunov method is applied to SPH instead of artificial dissipation terms. In the…
We construct a new Godunov type relativistic hydrodynamics code in Milne coordinates, using a Riemann solver based on the two-shock approximation which is stable under the existence of large shock waves. We check the correctness of the…
Recently developed concept of dissipative measure-valued solution for compressible flows is a suitable tool to describe oscillations and singularities possibly developed in solutions of multidimensional Euler equations. In this paper we…
Aquatic locomotion is a classic fluid-structure interaction (FSI) problem of interest to biologists and engineers. Solving the fully coupled FSI equations for incompressible Navier-Stokes and finite elasticity is computationally expensive.…
We solve the relativistic Riemann problem in viscous matter using the relativistic Boltzmann equation and the relativistic causal dissipative fluid-dynamical approach of Israel and Stewart. Comparisons between these two approaches clarify…