Abstract
An original strategy to address hydrodynamic flow was recently proposed through a high-order weakly-compressible Cartesian grid approach [1]. The method, named Weakly-Compressible Cartesian hydrodynamics (WCCH), is based on a fully-explicit temporal scheme for solving the Navier-Stokes equations while implicit incompressible schemes are usually preferred in the literature to address such flows. The present study aims to position and compare the WCCH method with a standard incompressible formulation. To this end, an incompressible scheme has been implemented in the same numerical framework. As far as possible, the algorithm used in the incompressible approach has been designed to be the same as (or close to) the one used in the weakly-compressible approach. In particular, high-order schemes for spatial and time discretization are employed. Pros and cons for each formulation are discussed in conjunction with a series of test cases on extensive criteria including implementation convenience, easy use of mesh refinement, convergence order and accuracy, numerical diffusion, parallel CPU scaling for high performance computing, etc. These comparisons demonstrate the relevance of the incompressible approach, at least for the selected test cases.
Highlights
While any fluid is compressible in reality, most liquid flow display negligible density variations and the fluid can be considered as incompressible
When Dirichlet boundary conditions are applied to the velocity, the linear system related to the Pressure Poisson Equation is singular since pressure is only determined up to a constant value
Incompressible and weakly-compressible schemes for hydrodynamic flows have been compared within the Finite Volume framework
Summary
While any fluid is compressible in reality, most liquid flow display negligible density variations and the fluid can be considered as incompressible. Compressible approaches are often ill-adapted to quasi-incompressible hydrodynamics (corresponding to low Mach number flows) Explicit algorithms can efficiently run on distributed memory architectures with an arbitrary high number of computational cores while maintaining good scaling properties (see [5] for the SPH method) These observations led us to develop the WCCH method to address hydrodynamic flow. To the best of our knowledge, there is no equivalent comparison between weakly-compressible and incompressible approaches in the Finite Volume framework, especially in presence of high-order schemes
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