Viscous vortex domains method

Viscous vortex domains (VVD) method is a mesh-free method of computational fluid dynamics for directly numerically solving 2D Navier-Stokes equations in Lagrange coordinates . It doesn't implement any turbulence model and free of arbitrary parameters. The main idea of this method is to present vorticity field with discrete regions (domains), which travel with diffusive velocity relatively to fluid and conserve their circulation. The same approach was used in Diffusion Velocity method of Ogami and Akamatsu , but VVD uses other discrete formulas

Features

The VVD method deals with viscous incompressible fluid. The viscosity and density of fluid is considered to be constant. Method can be extended for simulation of heat conductive fluid flows (viscous vortex-heat domains method)

The main features are:

• Direct solving Navier-Stokes equations (DNS)
• Calculation of the friction force at the body surfaces
• Proper description of the boundary layers (even turbulent)
• Infinite computation region
• Convenient simulation of deforming boundaries
• Investigation of the flow-structure interaction, even in case of zero mass
• Rather low numerical diffusion

Governing equations

The VVD method is based on a theorem, that circulation in viscous fluid is conserved on contours travelling with speed

$\mathbf {u} =\mathbf {V} +\mathbf {V} _{d}$, $\mathbf {V} _{d}=-\nu {\dfrac {\nabla \mathbf {\Omega } }{|\mathbf {\Omega } |}}$, $\mathbf {\Omega } =[\nabla \times \mathbf {V} ]$,

where V is fluid velocity, V_d — diffusion velocity, ν — kinematic viscosity.