The solution of the Navier-Stokes equation with the aid of a fully implicit iteration procedure

Computational difficulties arise in connection with the numerical solution of the Navier-Stokes equation in the three-dimensional case. These difficulties are related to the unstable behavior of the Navier-Stokes equation under conditions involving small coefficients of viscosity and large Reynolds numbers. The implementation of iteration methods in which convective and frictional terms are approximated implicitly, while pressure terms are approximated explicitly, can be very expensive because of the extensive computations required. The present investigation is, therefore, concerned with the employment of a fully implicit solution procedure involving the direct solution of the linear Navier-Stokes equation at each iteration step. The described solution procedure can be employed for studies involving steady and unsteady conditions. It is found to be very effective if the required computer storage capacity is available. The introduced monotonic approximations of the convective terms make it possible to compute solutions also for small coefficients of viscosity and large Reynolds numbers.