engleski

A Rapidly Convergent Algorithm For The Solution Of Navier-Stokes Equations

In this paper a novel pressure-velocity coupling algorithm for the solution of the Navier-Stokes equations by finite volume method on collocated grids is presented. In order to achieve pressure-velocity coupling, SIMPLE-like methods generally combine an approximate divergence of the pressure gradient field obtained from the momentum equations and the continuity equation. In formulations on collocated grids, the working variables are cell velocity components and cell pressure, while in order to suppress checker-board solutions, the cell face mass fluxes used in continuity equation are obtained by using special interpolations. The convergence rate of SIMPLE-like methods strongly rely on under-relaxation factor values, especially in segregated algorithm formulations. Compared to SIMPLE-like methods, novel pressure-velocity coupling method presented in this paper has several fundamental differences. Novel method uses cell face mass fluxes as working variables and irrotationality condition for the pressure gradient, while the cell velocity components are obtained by using the continuity equation. The resulting new pressure-velocity coupling algorithm approaches the final solution in an segregated iterative procedure by correcting cell face mass fluxes until the pressure gradient field becomes irrotational. The mass fluxes corrections applied in the new algorithm preserve the solution of the continuity equation, so that continuity equation has to be solved only once, at the beginning of the iteration procedure. Due the presented properties, the new algorithm ''naturally'' bypasses the checker-board problem in the collocated variable arrangement and doesn't require a stabilization procedure in the iterative solution process. The new pressure-velocity coupling algorithm was coded into own computer program and compared with the SIMPLE algorithm implemented within a commercial software package. The conducted tests covered 2D and 3D incompressible, inviscid and laminar flow problems having various boundary conditions and grid sizes and steady free convection problems solved using Boussinesq approximation. In conducted tests, the convergence rate of the new algorithm showed to be independent on grid size. In strict comparisons performed, both algorithms used same differencing scheme and identical grids. The new pressure-velocity algorithm shows a significantly higher convergence rate and CPU time efficiency.

Computational Fluid Dynamics; Finite Volume Method; Unstructured Grid; Pressure-Velocity Coupling; Segregated Method; Method Of Loops

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