Analysis of Algebraic Chorin Temam splitting for incompressible NSE and comparison to Yosida methods

Highlights

• ACT splitting can preserve the unconditional stability of BDF2-FEM and BE-FEM methods.

• Analysis includes incremental formulation and pressure correction for higher accuracy.

• We show ACT methods preserve the FEM divergence constraint.

• Our analysis is in the function space setting with appropriate norms.

• We give results of several numerical tests that compare Yosida and ACT.

Abstract

Algebraic splitting methods are a common approach to solving the saddle point linear systems that arise at each time step of an incompressible flow simulation. There are two main classes of these methods, those of Yosida-type and those of Algebraic Chorin Temam (ACT)-type, with the Yosida methods being predominantly used in practice. We show herein, through new analysis and extensive numerical testing, that ACT methods that include the viscous term stiffness matrix in the modified A-block are unconditionally stable and can be superior to Yosida methods in a range of problems. Particular situations where the ACT-type solvers are advantageous include problems where numerical stability is a concern, as well as problems where strong enforcement of the divergence constraint is important.