Temporal accuracy of FastRK3

Abstract

Standard third-order Runge-Kutta (RK3) can solve the incompressible Navier-Stokes equations with third-order accuracy, but does so by solving the Poisson equation for pressure at each of its three sub-steps. FastRK3 is a computational method for solving the incompressible Navier-Stokes equations in curvilinear coordinates over an orthogonal computational grid and is build upon the standard RK3 method. It solves the Poisson equation for pressure only once per time step. This implies that FastRK3 saves 66.6% of computational time standard RK3 spends solving the Poisson equation. The present thesis provides an analytical proof for the order of accuracy of FastRK3 and proves that it maintains third- order accuracy for free shear flows. The analytical proof is then validated numerically by performing the temporal accuracy analysis of FastRK3 for the Taylor-Green vortex flow.