Numerical Solution of the Navier-Stokes Equations

A finite-difference method for solving the time-dependent Navier-Stokes equations for an incompressible fluid is introduced.This method uses the primitive variables, i.e. the velocities and the pressure, and is equally applicable to problems in two and three space dimensions.Test problems are solved, and an application to a three-dimensional convection problem is presented.Introduction.The equations of motion of an incompressible fluid arewhere Ui are the velocity components, p is the pressure, p0 is the density, Ei are the components of the external forces per unit mass, v is the coefficient of kinematic viscosity, t is the time, and the indices i, j refer to the space coordinates Xi, x, i, j = 1, 2, 3. d, denotes differentiation with respect to Xi, and dt differentiation with respect to the time t.The summation convention is used in writing the equations.