Splitting scheme for poroelasticity and thermoelasticity problems

P. N. Vabishchevich   ; M. V. Vasil'eva   ; A. E. Kolesov

Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 54 (2014) no. 8, pp. 1345-1355

Résumé

Boundary value problems in thermoelasticity and poroelasticity (filtration consolidation) are solved numerically. The underlying system of equations consists of the Lamé stationary equations for displacements and nonstationary equations for temperature or pressure in the porous medium. The numerical algorithm is based on a finite-element approximation in space. Standard stability conditions are formulated for two-level schemes with weights. Such schemes are numerically implemented by solving a system of coupled equations for displacements and temperature (pressure). Splitting schemes with respect to physical processes are constructed, in which the transition to a new time level is associated with solving separate elliptic problems for the desired displacements and temperature (pressure). Unconditionally stable additive schemes are constructed by choosing a weight of a three-level scheme.

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