Consistent splitting SAV schemes for finite element approximations of incompressible flows

Computer Methods in Applied Mechanics and Engineering, vol. 446, pp. 118240

Abstract

Consistent splitting schemes are among the most accurate pressure segregation methods, incurring no splitting errors or spurious boundary conditions. Nevertheless, their theoretical properties are still only partially understood, especially when finite elements are used for the spatial discretisation. This work proposes a simple scalar auxiliary variable (SAV) technique that, when combined with standard finite elements in space, guarantees unconditional stability for first- and second-order consistent splitting schemes. The framework is implicit-explicit (IMEX) and only requires solving (vector-valued) linear transport equations and a pressure Poisson problem per time step. Furthermore, pressure stability is attained with respect to a stronger norm than in classical projection schemes, which allows circumventing the inf-sup condition and using, for example, equal-order velocity-pressure pairs. The accuracy of the new framework is assessed through numerical examples.

Authors 1

1. Douglas R. Q. Pacheco corresponding Aachen Center for Simulation and Data Science Chair for Computational Analysis of Technical Systems (CATS) Chair of Methods for Model‐based Development in Computational Engineering

   RWTH Aachen University

   Affiliation as printed

   Center for Simulation and Data Science (JARA-CSD), RWTH Aachen University, Germany

   Chair for Computational Analysis of Technical Systems, RWTH Aachen University, Germany

   Chair of Methods for Model-based Development in Computational Engineering, RWTH Aachen University, Germany