The solution of the NavierStokes equation with the aid of a fully implicit iteration procedure
Abstract
Computational difficulties arise in connection with the numerical solution of the NavierStokes equation in the threedimensional case. These difficulties are related to the unstable behavior of the NavierStokes 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 NavierStokes 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.
 Publication:

Zeitschrift Angewandte Mathematik und Mechanik
 Pub Date:
 1984
 DOI:
 10.1002/zamm.19840640604
 Bibcode:
 1984ZaMM...64..221Z
 Keywords:

 Computational Fluid Dynamics;
 Iterative Solution;
 NavierStokes Equation;
 Algebra;
 Algorithms;
 Finite Difference Theory;
 Linear Equations;
 Fluid Mechanics and Heat Transfer