Related papers: Scalable explicit implementation of anisotropic di…
Due to the prevalence of magnetic fields in astrophysical environments, magnetohydrodynamic (MHD) simulation has become a basic tool for studying astrophysical fluid dynamics. To further advance the precision of MHD simulations, we have…
Numerical schemes used for the integration of complex flow simulations should provide accurate solutions for the long time integrations these flows require. To this end, the performance of various high-order accurate numerical schemes is…
This is the second paper in a series in which we develop machine learning (ML) moment closure models for the radiative transfer equation (RTE). In our previous work \cite{huang2021gradient}, we proposed an approach to directly learn the…
Discrete diffusion models have emerged as a powerful generative modeling framework for discrete data with successful applications spanning from text generation to image synthesis. However, their deployment faces challenges due to the high…
We present MDIRK: a Multifluid second-order Diagonally-Implicit Runge-Kutta method to study momentum transfer between gas and an arbitrary number ($N$) of dust species. The method integrates the equations of hydrodynamics with an Implicit…
In this work, we present a modification of explicit Runge-Kutta temporal integration schemes that guarantees the preservation of any locally-defined quasiconvex set of bounds for the solution. These schemes operate on the basis of a…
We derive a consistent set of moments equations for CR-magnetohydrodynamics, assuming a gyrotropic distribution function (DF). Unlike previous efforts we derive a closure, akin to the M1 closure in radiation hydrodynamics (RHD), that is…
A mixed accuracy framework for Runge--Kutta methods presented in Grant [JSC 2022] and applied to diagonally implicit Runge--Kutta (DIRK) methods can significantly speed up the computation by replacing the implicit solver by less expensive…
The Runge--Kutta discontinuous Galerkin (RKDG) method is a high-order technique for addressing hyperbolic conservation laws, which has been refined over recent decades and is effective in handling shock discontinuities. Despite its…
Context. The magnetic field in the solar atmosphere continually reconnects and accelerates charged particles to high energies. Simulations of the atmosphere in three dimensions that include the effects of accelerated particles can aid our…
Finite element discretization of time dependent problems also require effective time-stepping schemes. While implicit Runge-Kutta methods provide favorable accuracy and stability problems, they give rise to large and complicated systems of…
We propose a new Eulerian-Lagrangian Runge-Kutta finite volume method for numerically solving convection and convection-diffusion equations. Eulerian-Lagrangian and semi-Lagrangian methods have grown in popularity mostly due to their…
The choice of numerical integrator in approximating solutions to dynamic partial differential equations depends on the smallest time-scale of the problem at hand. Large-scale deformations in elastic solids contain both shear waves and bulk…
Low-storage explicit Runge-Kutta schemes are particularly popular for the numerical integration of time-dependent partial differential equations based on the method-of-lines due to their efficiency and their reduced memory requirements. We…
We study in this paper three variants of the high-order Discontinuous Galerkin (DG) method with Runge-Kutta (RK) time integration for the induction equation, analysing their ability to preserve the divergence free constraint of the magnetic…
Anisotropic diffusion is imperative in understanding cosmic ray diffusion across the Galaxy, the heliosphere, and the interplay of cosmic rays with the Galactic magnetic field. This diffusion term contributes to the highly stiff nature of…
We present in this paper the numerical treatment of the coupling between hydrodynamics and radiative transfer. The fluid is modeled by classical conservation laws (mass, momentum and energy) and the radiation by the grey moment $M_1$…
This work presents algorithms for the efficient implementation of discontinuous Galerkin methods with explicit time stepping for acoustic wave propagation on unstructured meshes of quadrilaterals or hexahedra. A crucial step towards…
We propose a second-order implicit-explicit (IMEX) time-stepping scheme for the isentropic, compressible Cahn-Hilliard-Navier-Stokes equations discretized on staggered (MAC) grids. The scheme is based on finite difference approximations…
New implicit and implicit-explicit time-stepping methods for the wave equation in second-order form are described with application to two and three-dimensional problems discretized on overset grids. The implicit schemes are single step,…