相关论文: A GPU-accelerated mixed-precision WENO method for …

In this work we construct a high-order, single-stage, single-step positivity-preserving method for the compressible Euler equations. Space is discretized with the finite difference weighted essentially non-oscillatory (WENO) method. Time is…

In this study, we introduce a tensor-train (TT) finite difference WENO method for solving compressible Euler equations. In a step-by-step manner, the tensorization of the governing equations is demonstrated. We also introduce…

This paper develops $P^K$-based non-central and central Runge-Kutta discontinuous Galerkin (DG) methods with WENO limiter for the one- and two-dimensional special relativistic magnetohydrodynamical (RMHD) equations, $K=1,2,3$. The…

We propose two new alternative numerical schemes to solve the coupled Einstein-Euler equations in the Generalized Harmonic formulation. The first one is a finite difference (FD) Central Weighted Essentially Non-Oscillatory (CWENO) scheme on…

As computational astrophysics comes under pressure to become a precision science, there is an increasing need to move to high accuracy schemes for computational astrophysics. Hence the need for a specialized review on higher order schemes…

We present a novel method that solves Teukolsky equations with the source to calculate radiation fluxes at infinity and event horizon for any perturbation fields of type-D black holes. For the first time, we use the confluent Heun function…

In this article we present a new family of high order accurate Arbitrary Lagrangian-Eulerian one-step WENO finite volume schemes for the solution of stiff hyperbolic balance laws. High order accuracy in space is obtained with a standard…

Recently a splitting approach has been presented for the simulation of sonic-boom propagation. Splitting methods allow one to divide complicated partial differential equations into simpler parts that are solved by specifically tailored…

The detection of gravitational waves resulting by the LIGO-Virgo-Kagra collaboration has inaugurated a new era in gravitational physics, providing an opportunity to test general relativity and its modifications in the strong gravity regime.…

Mixed-precision computing has the potential to significantly reduce the cost of exascale computations, but determining when and how to implement it in programs can be challenging. In this article, we propose a methodology for enabling…

In this paper, we utilize the maximum-principle-preserving flux limiting technique, originally designed for high order weighted essentially non-oscillatory (WENO) methods for scalar hyperbolic conservation laws, to develop a class of high…

Observation and characterisation of gravitational waves from binary black holes requires accurate knowledge of the expected waveforms. The late inspiral and merger phase of the waveform is obtained through direct numerical integration of…

This work characterizes the structure of third and forth order WENO weights by deducing data bounded condition on third order polynomial approximations. Using these conditions, non-linear weights are defined for third and fourth order data…

In our latest studies, by introducing the novel order-preserving (OP) criterion, we have successfully addressed the widely concerned issue of the previously published mapped weighted essentially non-oscillatory (WENO) schemes that it is…

Based on the understandings regarding linear upwind schemes with flux splitting to achieve free-stream preservation (Q. Li, etc. Commun. Comput. Phys., 22 (2017) 64-94), a series of WENO interpolation-based and upwind-biased nonlinear…

We present a new version of conservative ADER-WENO finite volume schemes, in which both the high order spatial reconstruction as well as the time evolution of the reconstruction polynomials in the local space-time predictor stage are…

This paper developes Runge-Kutta $P^K$-based central discontinuous Galerkin (CDG) methods with WENO limiter to the one- and two-dimensional special relativistic hydrodynamical (RHD) equations, $K=1,2,3$. Different from the non-central DG…

An extreme mass ratio inspiral takes place when a compact stellar object is inspiraling into a supermassive black hole due to gravitational radiation reaction. Gravitational waves (GWs) from this system can be calculated using the Teukolsky…

In this paper we present a new family of high order accurate Arbitrary-Lagrangian-Eulerian (ALE) one-step ADER-WENO finite volume schemes for the solution of nonlinear systems of conservative and non-conservative hyperbolic partial…

The long-time evolution of extreme mass-ratio inspiral systems requires minimal phase and dispersion errors to accurately compute far-field waveforms, while high accuracy is essential near the smaller black hole (modeled as a Dirac delta…