Pressure Solver Research Articles

Multigrid preconditioned Krylov subspace methods for three-dimensional numerical solutions of the incompressible Navier–Stokes equations

We consider numerical methods for the incompressible Reynolds averaged Navier–Stokes equations discretized by finite difference techniques on non-staggered grids in body-fitted coordinates. A segregated approach is used to solve the pressure–velocity coupling problem. Several iterative pressure linear solvers including Krylov subspace and multigrid methods and their combination have been developed to compare the efficiency of each method and to design a robust solver. Three-dimensional numerical experiments carried out on scalar and vector machines and performed on different fluid flow problems show that a combination of multigrid and Krylov subspace methods is a robust and efficient pressure solver.

Preferential Flow-Paths Detection for Heterogeneous Reservoirs Using a New Renormalization Technique

We have devised a renormalization scheme which allows very fast determination of preferential flow-paths and of up-scaled permeabilities of 2D heterogeneous porous media. In the case of 2D log-normal and isotropically distributed permeability-fields, the resulting equivalent permeabilities are very close to the geometric mean, which is in good agreement with a rigorous result of Matheron. It is also found to work well for geostatistically anisotropic media when comparing the resulting equivalent permeabilities with a direct solution of the finite-difference equations. The method works exactly as King's does, although the renormalization scheme was modified to obtain tensorial equivalent permeabilities using periodic boundary conditions for the pressure gradient. To obtain an estimation of the local fluxes, the basic idea is that if at each renormalization iteration all the intermediate renormalized permeabilities are stored in memory, we are able to compute -- ad reversum -- an approximation of the small-scale flux map under a given macroscopic pressure gradient. The method is very rapid as it involves a number of calculations that vary linearly with the number of elementary grid blocks. In this sense, the renormalization algorithm can be viewed as a rapid approximate pressure solver. The ‘exact’ reference flow-rate map (for the finite-difference algorithm) was computed using a classical linear system inversion. It can be shown that the preferential flow paths are well detected by the approximate method, although errors may occur in the local flow direction.

Solution of the Navier‐Stokes equations by the spectral‐difference method

AbstractThe Jacobi polynomial collocation method is extended to two and three dimensions by superimposing the individual one‐dimensional expansions. Two innovative ideas are introduced in this article. The first is the cornerless/edgeless computational grid, and the second is the modified compressibility method, which is an iterative pressure solver. To evaluate the new method's applicability in solving the Navier‐Stokes equation, the lid‐driven cavity flow problem was solved. Two configurations were considered, the square cavity and the rectangular cavity with an aspect ratio of 2. A comparison of the center‐line velocity profiles from two‐ and three‐dimensional simulations at a Reynolds number of 1000 is provided for each of the configurations. The center‐line velocity comparisons showed good quantitative agreement with previous studies. © 1994 John Wiley & Sons, Inc.

A New Approach to Flow Simulation in Highly Heterogeneous Porous Media

Summary Applications are presented for a new numerical method—operator splitting on multiple grids (OSMG)—devised for simulations in heterogeneous porous media. A coarse-grid, finite-element pressure solver is interfaced with a fine-grid timestepping scheme. The CPU time for the pressure solver is greatly reduced and concentration fronts have minimal numerical dispersion.

Numerical Analysis on Outflow Boundary Condition of Vortex Convection with Uniform Mean Flow.

In order to investigate the fundamental rule for obtaining the adequate outflow velocity boundary condition of spatially developing unsteady flow, numerical simulation was performed for a simple model problem-a vortex convected with uniform mean flow by means of the pseudospectral matrix element (PSME) method. The results show that for the high Re number flows, the convective for mulation can be an accurate and a stable outflow velocity boundary condition if it is used together with the pressure solver enable to ensure divergence free on boundary.