Toward A Construction Of A Class Of Scheme Based On Wavelet Decomposition
Free (open access)
Y. Hamai & E. Outa
The paper proposes a new class of scheme based on wavelet decomposition. The field variables and the Navier-Stokes equations are projected on to the space spanned by the scaling functions. The scheme is first applied to the one-dimensional inviscid Burgers’ equation and the results show excellent agreements with the exact one. The one dimensional Euler equation with the Sod condition is also solved and the scheme captures the sharp shock front and contact discontinuity. The artificial dissipation terms are derived from physical analysis. The scheme, in addition, successfully solved the cavity flow problems with the Reynolds number up to 20000 with high accuracy. In the final part, a connection between the artificial dissipation and turbulence viscosity is discussed.