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Applications of an efficient low-mach algorithm to basic variable density flows

Time-accurate simulations are more and more required (e.g. LES of reacting flows). The generally applied pressure-correction schemes can no longer be used, due to lack of stability. Instabilities arise when the density variations are too large. In many combustion applications, high density ratios appear (e.g. for methane-air combustion at atmospheric pressure, density ratios in the order of 10 near the flamefront are normal). Some tried to circumvent the stability problem by applying (unphysical) rescaling of the time derivative of the density [1]. In [2], we showed that, for a non-reacting flow, a good constraint for the velocity field can be formulated, such that the solution is stable. In [3] the propositions of [2] were extended towards non-premixed combustion simulations, making use of the mixture fraction as a conserved variable. A pressure-correction algorithm was obtained which (1) conserves mass, (2) conserves fuel mass and (3) is stable and robust, without the need for (unphysical) underrelaxation. These three properties are obtained by introduction of a chemical operator H C as ρ = HC(ρξ) (ρ: density, ξ: mixture fraction). In case of pure mixing, the operator is linear. In case of combustion, however, HC is highly nonlinear. A discrete equation for the pressure, follows from a constraint on the velocity field by combining the discrete equations of continuity and mixture fraction. Due to the nonlinearity of HC, a non-linear equation for the pressure is obtained, which can be linearized around the predicted solution for the velocity field (u ∗ ):