Local Timestep Super-Time-Stepping Integration Methods Applied to Heat and Mass Transfer in Anisotropic Porous Media

Abstract

In fire safety problems, the simulation of the thermal degradation of anisotropic porous materials is complex due to the large amplitudes of time and space scales. Degraded areas where temperature increases and gas transport occurs might be very localised, sadly reducing the overall stability of numerical solvers and increasing the computation time. This can be mitigated thanks to Super-Time-Stepping methods, which are based on the use of a multi-step explicit scheme. In this study, these methods are first presented and their advantage to handle diffusion-advection problems such as the thermal degradation of anisotropic porous materials are emphasized on a simple use case. Then, a possible acceleration of the computation by using local timestep Super-Time-Stepping methods, particularly adapted to the heterogeneous problems previously mentioned, is discussed.

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