New semi-implicit method for solving the time-dependent conservation equations for incompressible flow

Abstract

A semi-implicit time integration scheme for the advection-diffusion equation, in which the advection terms are stepped forward in time using explicit Euler and the diffusion terms, which include a truncation error correction term, are integrated via the trapezoid rule, is described and demonstrated. In the extension to the Navier-Stokes and Boussinesq equations, all additional terms are integrated via explicit Euler.