Abstract

The present document is motivated by the development and the study of diffuse interface strategies which does not require the use of geometric interface reconstructions. A simple diffuse interface strategy is proposed for the multimaterial diffusion equation. While it is possible to consider only one average temperature per mixed cell, it is known [7] that standard harmonic or arithmetic homogeneous methods are not accurate on the simple 'sandwich' problem when working with coarse meshes. This has direct consequences for radiation-hydrodynamics applications. The numerical strategy presented here may be seen as a natural extension of standard homogeneous model and understood as if the diffusion operator is integrated on the global cell (not the materials) taking into account several temperature (one per material). Obviously, the accuracy of the presented method, compared to exact geometric reconstruction based ones, is expected to be lower in the general case. However, we believe that the simplicity of the methodology introduced in the present document, its robustness and practicality for real physical applications makes it interesting for a large audience.