A Conservative Pressure-Correction Method on Collocated Grid for Low Mach Number Flows

Abstract

A novel extension to SMAC scheme is proposed for variable density flows under low Mach number approximation. The algorithm is based on a predictor—corrector time integration scheme that employs a projection method for the momentum equation. A constant-coefficient Poisson equation is solved for the pressure following both the predictor and corrector steps to satisfy the continuity equation at each time step. The proposed algorithm has second order centrally differenced convective fluxes with upwinding based on Cell Peclet number while diffusive flux are viscous fourth order accurate. Spatial discretization is performed on a collocated grid system that offers computational simplicity and straight forward extension to curvilinear coordinate systems. The algorithm is kinetic energy preserving. Further in this paper robustness and accuracy are demonstrated by performing test on channel flow with non-Boussinesq condition on different temperature ratios

LES of Stably Stratified Flow with Varying Thermophysical Properties

“…This model has correct wall behavior for subgrid stresses near walls [21,22]. The employed scheme is an extension to the pressure correction method proposed for variable density flows under low Mach-number approximation by Anwer et al [23] and Yahya et al [24]. It utilizes a staggered grid approach with second-order time stepping of Adam Bashforth's method with only central differencing is utilized for evaluating convective terms, while viscous terms are implicitly calculated.…”

Interaction between turbulence and thermal radiation in combined heat transfer channel flows

“…On the basis of the previous discussions, when temperature variations in the system are large, fluid thermophysical properties, especially the density, are heavily affected by the temperature. To solve such a problem for an incompressible flow condition, the low Mach number approach is introduced and it has proved to be quite helpful . When the flow density is variable, the Navier‐Stokes equations, the internal energy equation, and also the equation of state must be solved simultaneously.…”

“…To solve such a problem for an incompressible flow condition, the low Mach number approach is introduced and it has proved to be quite helpful. [7][8][9] When the flow density is variable, the Navier-Stokes equations, the internal energy equation, and also the equation of state must be solved simultaneously.…”

“…As in the low‐speed turbulent flows, it covers large variations in density and eliminates the acoustic waves. As a result, there will be no need for extremely small time steps . The approach is applied to ideal gas flows with a Mach number of 0.3 or lower, without any limitation on the variations in temperature.…”

“…As a result, there will be no need for extremely small time steps. 9 The approach is applied to ideal gas flows with a Mach number of 0.3 or lower, without any limitation on the variations in temperature. Moreover, the accuracy of this approach in dealing with variable property flows is rather high.…”