Domain decomposition schemes for the Stokes equation

TL;DR

This paper develops unconditionally stable domain decomposition schemes for solving the Stokes equations in primitive variables, enabling efficient parallel computation for fluid dynamics problems.

Contribution

It introduces novel domain decomposition algorithms that are unconditionally stable and tailored for the Stokes system in primitive variables, advancing numerical methods for fluid flow simulations.

Findings

Schemes are unconditionally stable.

Applicable to primitive variable formulation of Stokes equations.

Facilitate parallel computation in fluid dynamics.

Abstract

Numerical algorithms for solving problems of mathematical physics on modern parallel computers employ various domain decomposition techniques. Domain decomposition schemes are developed here to solve numerically initial/boundary value problems for the Stokes system of equations in the primitive variables pressure-velocity. Unconditionally stable schemes of domain decomposition are based on the partition of unit for a computational domain and the corresponding Hilbert spaces of grid functions.