相关论文: Entropy-Preserving and Entropy-Stable Relaxation I…

An efficient multigrid framework is developed for the time marching of steady-state compressible flows with a spatially high-order ($p$-order polynomial) modal discontinuous Galerkin method. The core algorithm that based on a global…

In this paper, we develop a family of high order asymptotic preserving schemes for some discrete-velocity kinetic equations under a diffusive scaling, that in the asymptotic limit lead to macroscopic models such as the heat equation, the…

Many important initial value problems have the property that energy is non-increasing in time. Energy stable methods, also referred to as strongly stable methods, guarantee the same property discretely. We investigate requirements for…

This work aims to extend the residual distribution (RD) framework to stiff relaxation problems. The RD is a class of schemes which is used to solve hyperbolic system of partial differential equations. Up to our knowledge, it was used only…

Explicit stabilized methods are highly efficient time integrators for large and stiff systems of ordinary differential equations especially when applied to semi-discrete parabolic problems. However, when local spatial mesh refinement is…

The residual-based variational multiscale (VMS) formulation has achieved remarkable success in large-eddy simulation of turbulent flows. However, its temporal discretization has largely remained limited to second-order implicit schemes. The…

Differential equations arising in many practical applications are characterized by multiple time scales. Multirate time integration seeks to solve them efficiently by discretizing each scale with a different, appropriate time step, while…

Many HPC applications that solve differential equations rely on the Runge-Kutta family of methods for time integration. Among these methods, the fourth-order accurate RK4 scheme is especially popular. This time integration scheme requires…

We propose a new method that extends conservative explicit multirate methods to implicit explicit-multirate methods. We develop extensions of order one and two with different stability properties on the implicit side. The method is suitable…

In this article, a family of two- and three-stage explicit multiquadric (MQ) and inverse multiquadric (IMQ) radial basis functions (RBFs) Runge-Kutta methods are introduced for solving ordinary differential equations. These methods are…

Space discretization of some time-dependent partial differential equations gives rise to systems of ordinary differential equations in additive form whose terms have different stiffness properties. In these cases, implicit methods should be…

Statistical regression models whose mean functions are represented by ordinary differential equations (ODEs) can be used to describe phenomenons dynamical in nature, which are abundant in areas such as biology, climatology and genetics. The…

We discuss Implicit-Explicit (IMEX) Runge Kutta methods which are particularly adapted to stiff kinetic equations of Boltzmann type. We consider both the case of easy invertible collision operators and the challenging case of Boltzmann…

Explicit Runge-Kutta methods are classical and widespread techniques in the numerical solution of ordinary differential equations (ODEs). Considering partial differential equations, spatial semidiscretisations can be used to obtain systems…

In this work we present a class of high order unconditionally strong stability preserving (SSP) implicit multi-derivative Runge--Kutta schemes, and SSP implicit-explicit (IMEX) multi-derivative Runge--Kutta schemes where the time-step…

In the numerical solution of partial differential equations using a method-of-lines approach, the availability of high order spatial discretization schemes motivates the development of sophisticated high order time integration methods. For…

We put forward the use of total-variation-diminishing (or more generally, strong stability preserving) implicit-explicit Runge-Kutta methods for the time integration of the equations of motion associated with the semiconvection problem in…

A recently developed high-order implicit shock tracking (HOIST) framework for resolving discontinuous solutions of inviscid, steady conservation laws [41, 43] is extended to the unsteady case. Central to the framework is an optimization…

In this paper, we present a comprehensive long-time stability analysis of a second-order explicit exponential Runge--Kutta (ERK2) method for the Cahn--Hilliard (CH) equation. By employing Fourier spectral collocation in space and a…

Gradient flows of unit vector fields arise in a wide range of physical models such as harmonic map heat flows, nematic liquid crystals, and magnetization dynamics. Designing numerical schemes that simultaneously preserve the unit length…