• Corpus ID: 237563040

Maximum principle preserving space and time flux limiting for Diagonally Implicit Runge-Kutta discretizations of scalar convection-diffusion equations

  title={Maximum principle preserving space and time flux limiting for Diagonally Implicit Runge-Kutta discretizations of scalar convection-diffusion equations},
  author={Manuel Quezada de Luna and David I. Ketcheson},
We provide a framework for high-order discretizations of nonlinear scalar convection-diffusion equations that satisfy a discrete maximum principle. The resulting schemes can have arbitrarily high order accuracy in time and space, and can be stable and maximum-principle-preserving (MPP) with no step size restriction. The schemes are based on a two-tiered limiting strategy, starting with a high-order limiter-based method that may have small oscillations or maximum-principle violations, followed… 
Semi-implicit high resolution numerical scheme for conservation laws
We present novel semi-implicit schemes for numerical solution of time-dependant conservation laws. The core idea of the presented method consists of exploiting and approximating mixed partial


On maximum-principle-satisfying high order schemes for scalar conservation laws
Maximum-principle-satisfying High Order Finite Volume Weighted Essentially Nonoscillatory Schemes for Convection-diffusion Equations
It is shown that the same idea can be used to construct high order schemes preserving the maximum principle for two-dimensional incompressible Navier-Stokes equations in the vorticity stream-function formulation.
High Order Maximum Principle Preserving Finite Volume Method for Convection Dominated Problems
For the first time in the finite volume setting, a general proof is provided that the proposed flux limiter maintains high order accuracy of the original WENO scheme for linear advection problems without any additional time step restriction.
A Second-Order Maximum Principle Preserving Lagrange Finite Element Technique for Nonlinear Scalar Conservation Equations
This paper proposes an explicit, (at least) second-order, maximum principle sat- isfying, Lagrange finite element method for solving nonlinear scalar conservation equations. The technique is based on
Monolithic convex limiting in discontinuous Galerkin discretizations of hyperbolic conservation laws
  • H. Hajduk
  • Computer Science, Mathematics
    Comput. Math. Appl.
  • 2021
Strong stability preserving runge-kutta and multistep time discretizations
This comprehensive book describes the development of SSP methods, explains the types of problems which require the use of these methods and demonstrates the efficiency ofThese methods using a variety of numerical examples.