An artificial compressibility method for viscous incompressible and low Mach number flows

Abstract

SUMMARYWithin the framework of the pressure-based algorithm, an artificial compressibility method is developed on a non-orthogonal grid for incompressible and low Mach number fluid flow problems, using cellcentered finite-volume approximation. Resorting to the traditional pseudo-compressibility concept, the continuity constraint is perturbed by the time derivative of pressure, the physical relevance of which is to invoke matrix preconditionings. The approach provokes density perturbations, assisting the transformation between primitive and conservative variables. A dual-dissipation scheme for the pressure-velocity coupling is contrived, which has the expediences of greater flexibility and increased accuracy in a way similar to the monotone upstream-centered schemes for conservation laws approach. To account for the flow directionality in the upwinding, a rotational matrix is introduced to evaluate the convective flux. Numerical experiments in reference to a few well-documented laminar flows demonstrate that the entire contrivance expedites enhanced robustness and improved overall damping properties of the factored pseudo-time integration procedure.

Compound wall treatment with low‐Re turbulence model

“…Equations (25) and (26) are plotted in Figure 4. Despite satisfying the wall-limit and the fully turbulent phenomena, the blended curve exhibits a large discrepancy from the DNS data in the buffer region.…”

“…A cell-centered finite-volume scheme combined with an artificial compressibility approach is employed to solve the flow equations [25,26]. A fully upwinded second-order spatial differencing is applied to approximate the convective terms.…”

Assessment of two pressure-velocity coupling strategies for local meshless numerical method

“…After successful pressurevelocity iteration, the algorithm continues with the next time step. The LPVC approach is similar to the artificial compressibility method (ACM), which has been recently under intense research in connection with Finite Volume Method [26,27] and in connection with Finite Element Method [28]. A similar approach, in the framework of the FDM, is SOLA algorithm [29].…”

A simplified v2–f model for near‐wall turbulence

“…A multigrid method is utilized for the acceleration of convergence [34]. The basic implementation of the artificial compressibility method and associated features are described in [30,31]. Note that the elliptic relaxation Equations (8) and (19) are solved using TDMA.…”

“…A cell centred finite-volume scheme combined with an artificial compressibility approach is employed to solve the flow equations [30,31]. A fully upwinded second-order spatial differencing is applied to approximate the convective terms.…”