相关论文: Second Order Unconditional Positive Preserving Sch…
In \cite{BDM2003} the modified Patankar-Euler and modified Patankar-Runge-Kutta schemes were introduced to solve positive and conservative systems of ordinary differential equations. These modifications of the forward Euler scheme and…
In this paper, we perform stability analysis for a class of second and third order accurate strong-stability-preserving modified Patankar Runge-Kutta (SSPMPRK) schemes, which were introduced in [4,5] and can be used to solve convection…
Modified Patankar-Runge-Kutta (MPRK) methods preserve the positivity as well as conservativity of a production-destruction system (PDS) of ordinary differential equations for all time step sizes. As a result, higher order MPRK schemes do…
Non-local systems of conservation laws play a crucial role in modeling flow mechanisms across various scenarios. The well-posedness of such problems is typically established by demonstrating the convergence of robust first-order schemes.…
Positivity preservation of key physical quantities in the context of fluid flows, such as density and internal energy, is an essential property of a numerical scheme as otherwise the solution lacks physical relevance and has a not…
A well-balanced second-order finite volume scheme is proposed and analyzed for a 2 X 2 system of non-linear partial differential equations which describes the dynamics of growing sandpiles created by a vertical source on a flat, bounded…
Modified Patankar-Runge-Kutta (MPRK) schemes are numerical methods for the solution of positive and conservative production-destruction systems. They adapt explicit Runge-Kutta schemes to ensure positivity and conservation irrespective of…
Since almost twenty years, modified Patankar--Runge--Kutta (MPRK) methods have proven to be efficient and robust numerical schemes that preserve positivity and conservativity of the production-destruction system irrespectively of the time…
New time integration methods are proposed for simulating incompressible multiphase flow in pipelines described by the one-dimensional two-fluid model. The methodology is based on 'half-explicit' Runge-Kutta methods, being explicit for the…
In recent years, many positivity-preserving schemes for initial value problems have been constructed by modifying a Runge--Kutta (RK) method by weighting the right-hand side of the system of differential equations with solution-dependent…
Production-destruction systems (PDS) of ordinary differential equations (ODEs) are used to describe physical and biological reactions in nature. The considered quantities are subject to natural laws. Therefore, they preserve positivity and…
Higher-order time integration methods that unconditionally preserve the positivity and linear invariants of the underlying differential equation system cannot belong to the class of general linear methods. This poses a major challenge for…
In this study, we investigate the Shallow Water Equations incorporating source terms accounting for Manning friction and a non-flat bottom topology. Our primary focus is on developing and validating numerical schemes that serve a dual…
Many important applications are modelled by differential equations with positive solutions. However, it remains an outstanding open problem to develop numerical methods that are both (i) of a high order of accuracy and (ii) capable of…
Many practical problems can be described by second-order system $\ddot{q}=-M\nabla U(q)$, in which people give special emphasis to some invariants with explicit physical meaning, such as energy, momentum, angular momentum, etc. However,…
In this paper, we develop bound-preserving discontinuous Galerkin (DG) methods for chemical reactive flows. There are several difficulties in constructing suitable numerical schemes. First of all, the density and internal energy are…
Many important differential equations model quantities whose value must remain positive or stay in some bounded interval. These bounds may not be preserved when the model is solved numerically. We propose to ensure positivity or other…
In this paper, we develop parametrized positivity satisfying flux limiters for the high order finite difference Runge-Kutta weighted essentially non-oscillatory (WENO) scheme solving compressible Euler equations to maintain positive density…
In this paper, we develop a general framework for constructing higher-order, unconditionally energy-stable exponential time differencing Runge-Kutta methods applicable to a range of gradient flows. Specifically, we identify conditions…
We present a well-balanced finite volume solver for the compressible Euler equations with gravity where the approximate Riemann solver is derived using a relaxation approach. Besides the well-balanced property, the scheme is robust with…