A major limitation of the weakly compressible approaches to simulate incompressible flows is the appearance of artificial acoustic waves that introduce a large mass conservation error and lead to spurious oscillations in the force coefficients. In this work, we propose a non-homogeneous anisotropic bulk viscosity term to effectively damp the acoustic waves. By implementing this term in a computational framework based on the recently proposed general pressure equation, we demonstrate that the non-homogeneous and anisotropic nature of the term makes it significantly more effective than the isotropic homogeneous version widely used in the literature. Moreover, it is computationally more efficient than the pressure (or mass) diffusion term, which is an alternative mechanism used to suppress acoustic waves. We simulate a range of benchmark problems to comprehensively investigate the performance of the bulk viscosity on the effective suppression of acoustic waves, mass conservation error, order of convergence of the solver, and computational efficiency. The proposed form of the bulk viscosity enables fairly accurate modelling of the initial transients of unsteady simulations, which is highly challenging for weakly compressible approaches, and to the best of our knowledge, existing approaches can't provide an accurate prediction of such transients.
Hydrodynamic flow field and frictional resistance coefficient of a disk rotating steadily in a compressible fluid layer with odd viscosity on a rigid substrate
The Open University（开放大学）；Max Planck Institute for Dynamics and Self-Organization（马克斯·普朗克动力学与自组织研究所）
Analytical response functions for a compressible thin fluid layer with odd viscosity
The Open University（开放大学）；Max Planck Institute for Dynamics and Self-Organization (MPI–DS)（马克斯·普朗克动力学与自组织研究所）；Kyoto University（京都大学）；Wenzhou Institute, University of Chinese Academy of Sciences（中国科学院大学温州研究院）
Analysis of fluid velocity vector field divergence $\nabla\cdot\vec{u}$ in function of variable fluid density $ρ(\vec{x},t)\neq const$ and conditions for vanishing viscosity of compressible Navier-Stokes equations
Influence of viscosity on acoustic streaming in sessile droplets: an experimental and a numerical study with a Streaming Source Spatial Filtering (SSSF) method
High-amplitude free stream turbulence and surface roughness elements can excite a laminar boundary layer flow sufficiently to cause streamwise oriented vortices to develop. These vortices resemble elongated streaks having alternate spanwise variations of the streamwise velocity. Downstream, the vortices `wobble' through an inviscid secondary instability mechanism and, ultimately, transition to turbulence. We formulate an optimal control algorithm to suppress the growth rate of the streamwise vortex system. Considering a high Reynolds number asymptotic framework, we reduce the full compressible…
The effects of density and viscosity fluctuations on the total stress balance are identified and used to create a new mean velocity transformation for compressible boundary layers. This work is enabled by an extensive database of direct numerical simulations that incorporate wall-cooling, semi-local Reynolds numbers ranging from 800 to 34000, and Mach numbers up to 12. The role, significance and physical mechanisms connecting density and viscosity fluctuations to the momentum balance and to the viscous, turbulent and total stresses are presented,allowing the creation of generalized formulation…
We are concerned with the global existence theory for spherically symmetric solutions of the multidimensional compressible Euler equations with large initial data of positive far-field density. The central feature of the solutions is the strengthening of waves as they move radially inward toward the origin. Various examples have shown that the spherically symmetric solutions of the Euler equations blow up near the origin at certain time. A fundamental unsolved problem is whether the density of the global solution would form concentration to become a measure near the origin for the case when th…
