The mass diffusive model of Svärd simplified to simulate nearly incompressible flows

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• A novel model of nearly incompressible viscous flows based on the mass diffusive Svärd equations. • The model is mass and momentum conservative. • Poisson solver-free approach, algorithmic simplicity, easy parallelisation. • Adaptive speed of sound and time step. • Accurate results for 2D and 3D flow cases. 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 Re = 10 4 and the lid-driven cavity at 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 Re = 1600 is performed and shows a good agreement with reference data obtained with truly incompressible solver.