Hybrid Discretization Methods for Transient Numerical Simulation of Combustion in Porous Media

TL;DR

This paper introduces a hybrid discretization algorithm combining mixed finite element and finite volume methods for simulating transient combustion in porous media, demonstrating stability of reaction zones through numerical simulations.

Contribution

The paper presents a novel hybrid discretization approach for combustion in porous media, integrating mixed finite elements and finite volume methods with multigrid and Picard iterations.

Findings

Regions with different porosity stabilize the reaction zone

Numerical simulations validate the effectiveness of the hybrid method

The approach efficiently solves nonlinear coupled equations

Abstract

We present an algorithm for the numerical solution of the equations governing combustion in porous inert media. The discretization of the flow problem is performed by the mixed finite element method, the transport problems are discretized by a cell-centered finite volume method. The resulting nonlinear equations are lineararized with Newton's method, the linearized systems are solved with a multigrid algorithm. Both subsystems are recoupled again in a Picard iteration. Numerical simulations based on a simplified model show how regions with different porosity stabilize the reaction zone inside the porous burner.