Approximation particulaire des équations de Navier-Stokes bidimensionnelles. (Particle approximation of the two-dimensional Navier-Stokes equations). (French) Zbl 0619.76031

Lucquin-Desreux, B.

Rech. Aérosp. 1987, No. 4, 1-12 (1987).

A vortex method is used for the numerical simulation of two-dimensional incompressible unsteady viscous flows. The vorticity is discretized by particles and the velocity is then computed by the Biot Savart law. New regularized kernels with simple rational expression are determined in 2D and 3D and tested in the case of the two-dimensional Euler equations. Equations are solved by a splitting method: the convection is treated by a particle method while the diffusion is solved explicitly using the heat operator kernel.

MSC:

76D05	Navier-Stokes equations for incompressible viscous fluids
80A20	Heat and mass transfer, heat flow (MSC2010)
76R50	Diffusion
76M99	Basic methods in fluid mechanics

Keywords:

vortex method; numerical simulation; two-dimensional incompressible unsteady viscous flows; Biot Savart law; regularized kernels; two- dimensional Euler equations; splitting method; convection; particle method; diffusion; heat operator kernel