Splitting schemes for hyperbolic heat conduction equation

TL;DR

This paper develops and analyzes splitting schemes for the hyperbolic heat conduction equation, which models finite heat transfer velocity, ensuring stability and proposing new computational methods.

Contribution

It introduces additive splitting schemes for the hyperbolic heat conduction model, demonstrating their unconditional stability and providing new methods for solving related systems.

Findings

Unconditionally stable splitting schemes are established.

New splitting schemes for temperature and heat flux system are proposed.

The schemes are suitable for modeling finite heat transfer velocity.

Abstract

Rapid processes of heat transfer are not described by the standard heat conduction equation. To take into account a finite velocity of heat transfer, we use the hyperbolic model of heat conduction, which is connected with the relaxation of heat fluxes. In this case, the mathematical model is based on a hyperbolic equation of second order or a system of equations for the temperature and heat fluxes. In this paper we construct for the hyperbolic heat conduction equation the additive schemes of splitting with respect to directions. Unconditional stability of locally one-dimensional splitting schemes is established. New splitting schemes are proposed and studied for a system of equations written in terms of the temperature and heat fluxes.