Entropically damped artificial compressibility for the discretization corrected particle strength exchange method in incompressible fluid mechanics

Abstract

We present a consistent mesh-free numerical scheme for solving the incompressible Navier-Stokes equations. Our method is based on entropically damped artificial compressibility for imposing the incompressibility constraint explicitly, and the Discretization-Corrected Particle Strength Exchange (DC-PSE) method to consistently discretize the differential operators on mesh-free particles. We further couple our scheme with Brinkman penalization to solve the Navier-Stokes equations in complex geometries. The method is validated using the 3D Taylor-Green vortex flow and the lid-driven cavity flow problem in 2D and 3D, where we also compare our method with hr-SPH and report better accuracy for DC-PSE. In order to validate DC-PSE Brinkman penalization, we study flow past obstacles, such as a cylinder, and report excellent agreement with previous studies.

arXiv comment23 pages, 12 figures

References in corpus (6)

• SPH compressible turbulence
• Thermodynamic Theory of Incompressible Hydrodynamics
• Numerical simulations of unsteady viscous incompressible flows using general pressure equation
• A Fully Lagrangian Meshfree Framework for PDEs on Evolving Surfaces
• General and exact pressure evolution equation
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Cited by in corpus (1)

• Integrating Discrete Sub-grid Filters with Discretization-Corrected Particle Strength Exchange Method for High Reynolds Number Flow Simulations