DeepAI AI Chat
Log In Sign Up

Exponential time integrators for unsteady advection-diffusion problems on refined meshes

10/09/2020
by   M. A. Botchev, et al.
0

Time integration of advection dominated advection-diffusion problems on refined meshes can be a challenging task, since local refinement can lead to a severe time step restriction, whereas standard implicit time stepping is usually hardly suitable for treating advection terms. We show that exponential time integrators can be an efficient, yet conceptually simple, option in this case. Our comparison includes three exponential integrators and one conventional scheme, the two-stage Rosenbrock method ROS2 which has been a popular alternative to splitting methods for solving advection-diffusion problems.

READ FULL TEXT

page 1

page 2

page 3

page 4

07/06/2022

Exponential integrators for non-linear diffusion

The goal of this project is to compare the performance of exponential ti...
08/04/2020

A nonlinear weak constraint enforcement method for advection-dominated diffusion problems

We devise a stabilized method to weakly enforce bound constraints in the...
11/16/2022

Exponential methods for anisotropic diffusion

The anisotropic diffusion equation is of crucial importance in understan...
11/04/2020

Local Coarsening Algorithms on Adaptively Refined Meshes in 2D and Their Efficient Implementation in MATLAB

Adaptive meshing includes local refinement as well as coarsening of mesh...
10/25/2021

Partially Explicit Time Discretization for Nonlinear Time Fractional Diffusion Equations

Nonlinear time fractional partial differential equations are widely used...
12/08/2022

Interpolation Operators for parabolic Problems

We introduce interpolation operators with approximation and stability pr...