Wavelet basedlocal spectral element method (Method of finite subdomains)

The widespead availablity of parallelcomputers and their potential for the numerical solution of difficult-to-solve partialdifferential equations have led to a large amount of research in domaindecomposition methods, especially in CFD, where many applications involvecomplex geometries. The wavelet essentially-non-dispersive (WEND) scheme isconstructed by using the Discrete Singular Convolution (DSC) algorithm, whichrequires as little as 2.2 point per wavelength (PPW) for flowsimulations. For complex geometry, a wavelet based new

A close-up view gives fine flow details:

An other example we studied is the steadyflow of a staggered lid-driven cavity:

Fig1. The streamline forRe=100 Fig2: The vorticity for Re=100

**Here 5 subdomains are used forthe simulation.**

Thelocal spectral WEND scheme is also used for computing the fluid flowpatterns in a buoyancy driven cavity for a very high Rayleigh number (Ra=10^8).Simulation at this parameter is very close to the transition of naturalconvection into a turbulent flow, which can be construed as a very tough testfor any numerical scheme. The conventional local methods have reportedlyproduced spurious oscillations. DSC spatial discretization could quiteaccurately simulate the fluid flow features devoid of all the negative effects.

**References:**

**D.C. Wan, B.S.V. Patnaik and G.W. Wei, A new benchmark quality solution for the buoyancydriven cavity by discrete singular convolution, Numer. Heat Transfer B -Fundamentals , 40 , 199-228 (2001).**

**D.C. Wan, B.S.V. Patnaik and G.W. Wei, Discrete singular convolution-finite subdomain methodfor the solution of incompressible viscous flows, J. Comput. Phys. 180,229-255 (2002).**

**Y.C. Zhou, B. S. V. Patnaik, D.C. Wan andG. W. Wei, DSC solution for flow in a staggereddouble lid driven cavity, Int. J. Numer. Methods in Engng. , 57, 211-234(2003).**