A model of viscous gas flows has recently been proposed by Svärd (2018) [27] as a remedy to some physical inconsistencies of the compressible Navier-Stokes equations. We adopt and simplify the model to handle nearly incompressible flows by neglecting the energy conservation law and imposing the isothermal equation of state. For the sake of accuracy and computational efficiency, the artificial speed of sound and the time step are set adaptively during the simulation. The governing equations are solved using 2nd-order central schemes and the skew-symmetric forms are utilised for the hyperbolic terms. Since the explicit time integration is used and the pressure field is obtained from the density via the equation of state, no linear systems of equations need to be solved. Moreover, the use of two-point stencils for the discretisation of fluxes and ellipticity-free type of the governing equations make the model simple and efficient in the context of computer implementation and parallel execution. The analysis of accuracy, resolving power and compressible effects is done on the basis of two-dimensional flow simulations: the Taylor-Green vortex (TGV) at Re=300, the doubly periodic shear layer at $\text{Re}={10}^4$ and the lid-driven cavity at $\text{Re}={10}^3$. The Svärd model, due to the physically-based diffusive term present in the mass conservation equation, reveals to be more accurate than a similar model based on the Navier-Stokes equations, as shown by the error analysis in the 2D TGV case. For the cases studied, the proper value of the Mach number allowing to match the results with those obtained by means of a truly incompressible flow solver is estimated to be approximately 0.05. Direct numerical simulation of three-dimensional TGV at $\text{Re}=1600$ is performed and shows a good agreement with reference data obtained with truly incompressible solver.

Svärd (2018) [27] 最近提出了粘性气体流动模型，作为可压缩 Navier-Stokes 方程的一些物理不一致性的补救措施。我们通过忽略能量守恒定律和强加等温状态方程，采用并简化模型来处理几乎不可压缩的流动。为了精度和计算效率，在仿真过程中自适应地设置了人工声速和时间步长。控制方程使用二阶中心方案求解，双曲项使用斜对称形式。由于使用了显式时间积分，并且压力场是通过状态方程从密度获得的，因此不需要求解线性方程组。而且，使用两点模板来离散通量和控制方程的无椭圆类型使模型在计算机实现和并行执行的情况下简单有效。精度、分辨能力和可压缩效应的分析是在二维流动模拟的基础上进行的：Re=300 处的 Taylor-Green 涡流 (TGV)，双周期剪切层$\text{回覆}={10}^4$和盖子驱动的空腔$\text{回覆}={10}^3$. 由于质量守恒方程中存在基于物理的扩散项，Svärd 模型比基于 Navier-Stokes 方程的类似模型更准确，如 2D TGV 案例中的误差分析所示。对于所研究的案例，马赫数的适当值允许将结果与通过真正不可压缩流动求解器获得的结果相匹配，估计约为 0.05。三维 TGV 的直接数值模拟$\text{回覆}=1600$执行并显示与使用真正不可压缩求解器获得的参考数据的良好一致性。