A Upwind LowerUpper Algorithm for the Solution of Steady and Unsteady Incompressible NavierStokes Equations.
Abstract
An algorithm for the solution of steady and unsteady NavierStokes equations modeling incompressible fluids has been developed using the pseudo compressibility concept. The algorithm employs the finite volume, fluxvector splitting, third order upwind, lowerupper (LU) implicit scheme to solve the equations which have been cast in a curvilinear coordinate system. The upwinding is implemented using the fluxvector splitting. An approach is developed for splitting the incompressible inviscid flux vectors. This approach makes the direct application of flux vectorsplitting procedures, developed for compressible flow, possible. When used with the LU implicit scheme, it makes the scalar diagonal inversion possible without using diagonalization procedure. This significantly reduces the computational time required to solve the LU approximation. The approach also reduces the computational effort required to obtain the flux vectors and their jacobians. No additional dissipation terms are included in the scheme. The algorithm is validated by computing a number of twodimensional steady and unsteady flow problems. Both laminar and turbulent flows were considered. Comparison of the results obtained with existing numerical and analytical solutions and with experimental data shows good agreement. The algorithm is more efficient and has a better solution convergence rate compared to the recently developed diagonal LU and LUSGS algorithms.
 Publication:

Ph.D. Thesis
 Pub Date:
 1993
 Bibcode:
 1993PhDT.......205S
 Keywords:

 Physics: Fluid and Plasma; Engineering: Mechanical