Navier–Stokes Equations for Almost Incompressible Flow

The isentropic Navier–Stokes equations at low Mach numbers describe almost incompressible flow. By a variable transformation the equations take a symmetric form suitable for computation. Estimates of the solution and its derivatives are obtained for the linearized equations on domains with open boundaries. This is a necessary basis for the application of any numerical method whenever some part of the computational boundary is not a solid wall. A semi-implicit difference approximation is applied to the nonlinear equations for computation of flow over a backward-facing step.