Vortex methods for flows of variable density

Technical Report · Wed Jun 01 00:00:00 EDT 1983

OSTI ID:5336353

Anderson, C R

We present two numerical methods for calculating the motion of an incompressible, inviscid fluid of slightly varying density. The methods, both based on the vortex method developed by Chorin, are grid free and have no intrinsic source of numerical diffusion. We analyze the methods using techniques derived from the recent work on the convergence of the vortex method. We prove a convergence result for one method and prove a partial convergence result for the other method. We present an exact solution to the equations of motion for a fluid of variable density and use this solution to test both numerical methods. The test results indicate that the methods are stable and accurate. An application to the problem of calculating the motion of a 2-D thermal is also presented. The computational results indicate that the methods are suitable for calculating flows associated with thermal convection phenomena. In the course of our investigations of the motion of a 2-D thermal, we found significant computational evidence to suggest that a singularity develops in the flow in finite time. This singularity appears to be confined to a small set, possibly a point, and is characterized by an infinite value of vorticity there.

• Research Organization: Lawrence Berkeley Lab., CA (USA)
• DOE Contract Number: AC03-76SF00098
• OSTI ID: 5336353
• Report Number(s): LBL-16702; ON: DE84002915
• Country of Publication: United States
• Language: English

Related Subjects

640410* -- Fluid Physics-- General Fluid Dynamics
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
COMPUTER CALCULATIONS
CONVECTION
DIFFERENTIAL EQUATIONS
EQUATIONS
EQUATIONS OF MOTION
FLUID FLOW
INCOMPRESSIBLE FLOW
NUMERICAL SOLUTION
PARTIAL DIFFERENTIAL EQUATIONS
TWO-DIMENSIONAL CALCULATIONS
VORTEX FLOW