A Upwind Lower-Upper Algorithm for the Solution of Steady and Unsteady Incompressible Navier-Stokes Equations.
An algorithm for the solution of steady and unsteady Navier-Stokes equations modeling incompressible fluids has been developed using the pseudo compressibility concept. The algorithm employs the finite volume, flux-vector splitting, third order upwind, lower-upper (LU) implicit scheme to solve the equations which have been cast in a curvilinear coordinate system. The upwinding is implemented using the flux-vector splitting. An approach is developed for splitting the incompressible inviscid flux vectors. This approach makes the direct application of flux vector-splitting 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 two-dimensional 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 LU-SGS algorithms.
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- Physics: Fluid and Plasma; Engineering: Mechanical