Related papers: A "Neural" Riemann solver for Relativistic Hydrody…
Physics-informed neural network architectures have emerged as a powerful tool for developing flexible PDE solvers which easily assimilate data, but face challenges related to the PDE discretization underpinning them. By instead adapting a…
We present a novel methodology based on Physics-Informed Neural Networks (PINNs) for solving systems of partial differential equations admitting discontinuous solutions. Our method, called Gradient-Annihilated PINNs (GA-PINNs), introduces a…
This paper studies the two-stage fourth-order accurate time discretization \cite{LI-DU:2016} and applies it to special relativistic hydrodynamical equations. It is shown that new two-stage fourth-order accurate time discretizations can be…
In this paper we use the symmetry reduction method to obtain invariant solutions of the ideal magnetohydrodynamic equations in (3+1) dimensions. These equations are invariant under a Galilean-similitude Lie algebra for which the…
Numerical simulation of fluids plays an essential role in modeling many physical phenomena, such as weather, climate, aerodynamics and plasma physics. Fluids are well described by the Navier-Stokes equations, but solving these equations at…
We review recent interest in the relativistic Riemann problem as a method for generating a non-equilibrium steady state. In the version of the problem under con- sideration, the initial conditions consist of a planar interface between two…
An exact closure for hydrodynamic variables is rigorously derived from the linear Boltzmann kinetic equation. Our approach, based on spectral theory, structural properties of eigenvectors and the theory of slow manifolds, allows us to…
Radiative transfer and radiation hydrodynamics use the relativistic Boltzmann equation to describe the kinetics of photons. It is difficult to solve the six-dimensional time-dependent transfer equation unless the problem is highly symmetric…
Upcoming large-scale-structure surveys can shed new light on the properties of dark energy. In particular, if dark energy is a dynamical component, it must have spatial perturbations. Their behaviour is regulated by the speed of sound…
We compare here several modern versions of SPH with a particular focus on the impact of gradient accuracy. We examine specifically an approximation to the "linearly exact" gradients (aLE) with standard SPH kernel gradients and with linearly…
We present an algorithm for solving the radiative transfer problem on massively parallel computers using adaptive mesh refinement and domain decomposition. The solver is based on the method of characteristics which requires an adaptive…
We present an efficient and highly scalable geometric method for two-dimensional ideal fluid dynamics on the sphere. The starting point is Zeitlin's finite-dimensional model of hydrodynamics. The efficiency stems from exploiting a…
The large-scale simulation of dynamical systems is critical in numerous scientific and engineering disciplines. However, traditional numerical solvers are limited by the choice of step sizes when estimating integration, resulting in a…
Resolvent analysis is a powerful tool for studying coherent structures in turbulent flows. However, its application beyond canonical flows with symmetries that can be used to simplify the problem to inherently three-dimensional flows and…
There is great interest in numerical relativity simulations involving matter due to the likelihood that binary compact objects involving neutron stars will be detected by gravitational wave observatories in the coming years, as well as to…
A high-resolution finite volume method approach to incorporating time-dependent slip across rectangular subfaults when modeling general fault geometry is presented. The fault slip is induced by a modification of the Riemann problem to the…
Constrained optimization problems appear in a wide variety of challenging real-world problems, where constraints often capture the physics of the underlying system. Classic methods for solving these problems rely on iterative algorithms…
A third order shock-capturing numerical scheme for three-dimensional special relativistic magnetohydrodynamics (3-D RMHD) is presented and validated against several numerical tests. The simple and efficient central scheme described in Paper…
In this paper, the second in a series, we document the algorithms and solvers for compressible nonrelativistic hydrodynamics implemented in GenASiS (General Astrophysical Simulation System)---a new code being developed initially and…
We present an exact solution of the relativistic Boltzmann equation for a system undergoing boost-invariant longitudinal and azimuthally symmetric transverse flow ("Gubser flow"). The resulting exact non-equilibrium dynamics is compared to…