Enhancing the viscosity-splitting method to solve the time-dependent Navier–Stokes equations

Abstract

The viscosity-splitting (VS) scheme for solving the incompressible time-dependent Navier–Stokes equations consists to decouple the full problem into two easy subproblems to resolve. This method splits the nonlinearity (convection term) and the incompressibility into two different steps. As a result, every subproblem is easier to solve than the Navier–Stokes system. The semi-implicit approach is mostly used in the first step for the nonlinearity term and the intermediate velocity is calculated by dropping the pressure gradient. We then resolve a linear Stokes problem in the next step.We present a modified viscosity-splitting scheme (Incremental viscosity-splitting) (IVS) to improve this method. This scheme adds the gradient of the pressure (calculated at the previous time step) in the first step and modifies the Stokes equations in the second step to predict a better value of the intermediate velocity. A manufactured solution and two well-known benchmarks will be used to demonstrate the effectiveness of the suggested strategy.