Explicit Time Mimetic Discretiztions Of Wave Equations

TL;DR

This paper develops explicit time and staggered spatial discretizations for wave equations that preserve key properties like energy conservation, ensuring stability and mimicking continuum behavior in a discrete setting.

Contribution

It introduces a second-order accurate, mimetic spatial discretization combined with explicit leapfrog time schemes that conserve a discrete energy, enhancing stability and fidelity.

Findings

Discretizations are second order accurate and mimetic.

Conserved quantities guarantee stability under certain time step constraints.

Method closely mimics continuum wave properties in a discrete framework.

Abstract

This paper is part of a program to combine a staggered time and staggered spatial discretization of continuum wave equations so that important properties of the continuum that are proved using vector calculus can be proven in an analogous way for the discretized system. The spatial discretizations are second order accurate and mimetic. The time discretizations second are order accurate explicit leapfrog schemes. The discretizations have a conserved quantity that guarantees stability for a reasonable constraint on the time step. The conserved quantities are closely related to the energy for the continuum equations.