Meshfree Modeling and Analysis

Fluid Dynamics Problem

Reference [3] describes numerical properties of the RFM applied to incompressible fluid dynamics problems. The paper discusses accuracy and convergence of the RFM solutions using as an example the stream function approach as well as the artificial compressibility approach. The latter leads to direct solution of the Navier-Stokes equations. Figure 1 shows the stream function and the distribution of absolute value of the velocity vector inside the channel for Reynolds numbers Re=100 and Re=400. Figure 2 presents the distributions of the velocity components and pressure around the car inside a wind tunnel computed by direct solution of the Navier-Stokes equations via the R-function meshfree method. (a) (b) (c) (d) Figure 1: (a) Stream function for Re=100; (b) absolute value of the velocity vector for Re=100; (c) Stream function for Re=400; (d) absolute value of the velocity vector for Re=400 (a) (b) (c) Figure 2: Distributions of (a) horizontal, (b) vertical components of the velocity vector, and (d) pressure around the car inside a wind tunnel

References

[1] V.L. Rvachev, T.I. Sheiko, V. Shapiro, I. Tsukanov, Transfinite Interpolation Over Implicitly Defined Sets, Computer Aided Geometric Design, Vol. 18, No. 4, 2001, pp.195-220 [2] V.L.Rvachev, T.I.Sheiko, V.Shapiro and I.Tsukanov, On Completeness of RFM Solution Structures, Computational Mechanics, special issue on meshfree methods, Vol. 25, 2000, pp. 305-316 [3] I.Tsukanov, V.Shapiro, S.Zhang, A Meshfree Method for Incompressible Fluid Dynamics Problems, International Journal for Numerical Methods in Engineering. Submitted for publication