Flow over a circular cylinder simulated by virtual interpolation point method


Incompressible Navier-Stkoes equations:

$\frac{\partial \mathbf{u}}{\partial t} + (\mathbf{u}\cdot \nabla \mathbf{u}) + \nabla p = \nu \nabla^2 \mathbf{u}$
$\nabla\cdot \mathbf{u} = 0$
where $\mathbf{u}$ is velocity, $p$ is pressure, and $\nu$ is kinetic viscosity.

Virtual interpolation point (VIP) method

In VIP method, virtual staggered structure is formed for the velocity and pressure from the actual computation node set. The VIP method by a point collocation scheme is well suited for meshfree scheme because the approximation comes from smooth kernels and kernels can be differentiate directly. This paper highlights our contribution to a stable flow computation without explicit structure of staggered grid. Our method eliminate the need to construct explicitly the staggered grid. Instead virtual interpolation nodes play key roles in discretizing the conservative quantities of the Stokes equations.

Numerical example

Figure 1. Evolution of vorcity for $Re=1,000$.
Figure 2. Evolution of vorcity for $Re=10,000$.
Figure 3. Evolution of vorcity for $Re=100,000$ ($10^5$).