Development of artificial compressibility method with elliptic relaxation approach

Abstract

An artificial compressibility (AC) method resorting to the pressure-based algorithm is developed on a non-orthogonal non-staggered grid using a cell-centered finite-volume Δ-approximation for incompressible fluid flow problems. A pressure time-derivative is used to perturb the equation of continuity. This artifact provokes a density preconditioning which transforms conservative variables to primitive ones; the physical relevance of density preconditioning signifies to convoke compatible linearizations of residuals in collaboration with an AC parameter. The avoidance of pressure-velocity decoupling is enhanced by a consistently formulated cell-face dissipation approach, preserving an increased accuracy with a greater flexibility analogous to the MUSCL (monotone upstream-centered schemes for conservation laws) approach. An elliptic-relaxation scheme having accountability to promoting anisotropic diffusion coefficients is applied to smooth out the pressure residual. Numerical experiments dictate that pertaining to the pseudo-time integration method, the overall contrivance is benefited with an enhanced robustness having sensible oscillation damping characteristics.