A relaxation method for steady NavierStokes equations, based on fluxvector splitting
Abstract
Based on the example of CauchyRiemann equations, the fluxvector splitting method is illustrated for systems of firstorder equations. It is shown that for this linear elliptic system of equations, fluxvector splitting combined with upwind differencing results in discrete equations which can be solved by relaxation methods. Furthermore, it is shown how the same splitting can be used on the hybrid firstorder (subprincipal) part of the steady NavierStokes equations in a primitive variable form. By the use of central difference discretizations on the second order (principal) part, the resulting set of discrete equations can be solved by relaxation methods. A computational example of a backwardfacing step problem is given.
 Publication:

IN: Numerical methods in laminar and turbulent flow; Proceedings of the Fourth International Conference
 Pub Date:
 1985
 Bibcode:
 1985nmlt.proc..527D
 Keywords:

 CauchyRiemann Equations;
 Computational Fluid Dynamics;
 NavierStokes Equation;
 Relaxation Method (Mathematics);
 Steady Flow;
 Boundary Value Problems;
 Computational Grids;
 Elliptic Differential Equations;
 Linear Equations;
 Splitting;
 Vectors (Mathematics);
 Fluid Mechanics and Heat Transfer