Over the past two decades, there has been much development in discontinuous Galerkin methods for incompressible flows and for compressible flows with a positive Mach number, but almost no attention has been paid to variable-density flows at low speeds. This paper presents a pressure-based discontinuous Galerkin method for flow in the low-Mach number limit. We use a variable-density pressure correction method, which is simplified by solving for the mass flux instead of the velocity. The fluid properties do not depend significantly on the pressure, but may vary strongly in space and time as a function of the temperature.

We pay particular attention to the temporal discretization of the enthalpy equation, and show that the specific enthalpy needs to be ‘offset’ with a constant in order for the temporal finite difference method to be stable. We also show how one can solve for the specific enthalpy from the conservative enthalpy transport equation without needing a predictor step for the density. These findings do not depend on the spatial discretization.

A series of manufactured solutions with variable fluid properties demonstrate full second-order temporal accuracy, without iterating the transport equations within a time step. We also simulate a Von Kármán vortex street in the wake of a heated circular cylinder, and show good agreement between our numerical results and experimental data.

在过去的二十年中，不连续的Galerkin方法在不可压缩流和马赫数为正的可压缩流方面取得了很大进展，但几乎没有关注低速下的可变密度流。本文提出了一种基于压力的不连续Galerkin方法，用于低马赫数极限的流动。我们使用可变密度压力校正方法，该方法通过求解质量通量而不是速度来简化。流体性质不显着取决于压力，但是在空间和时间上可以随温度变化很大。

我们特别注意焓方程的时间离散化，并表明为了使时间有限差分方法稳定，需要将特定的焓“抵消”一个常数。我们还展示了如何能够从保守的焓传递方程式中求解比焓而无需预测密度的步骤。这些发现不依赖于空间离散化。

一系列具有可变流体特性的制造解决方案证明了完全的二阶时间精度，而无需在一个时间步内迭代传输方程。我们还模拟了加热的圆柱体后的VonKármán涡街，并显示了我们的数值结果和实验数据之间的良好一致性。