The Generalized Boundary Element Approach to Viscous Flow Problems by Using the Time Splitting Technique
We present a new attempt by means of the generalized boundary element approach to solve an unsteady-state problem of viscous fluid flow. This approach is based on the well-known Fractional Step (FS) scheme which is one of the time splitting techniques. The fundamental equations are split into the advection-diffusion-type equation and the linear Euler-type ones. The advection-diffusion-type equation is transformed into the integral representation with the fundamental solution for the Laplace operator. The Poisson equation which is derived by applying some manipulations to the Euler-type equations is also solved by using the generalized boundary element method. Numerical results of the driven cavity flow demonstrate the accuracy and applicability of our method.
Unable to display preview. Download preview PDF.
- 3.Thomasset, F.: Implementation of Finite Element Methods for Navier-Stokes Equations, Springer-Verlag, 1981.Google Scholar
- 8.Tosaka, N.; Kakuda, K.: Newtonian and Non-Newtonian Unsteady Flow Problems, in Chapter 5 of Boundary Element Methods in Nonlinear Fluid Dynamics, Developments in Boundary Element Methods 6 (Eds., P.K. Banerjee and L. Morino), pp.151-181, Elsevier Applied Science, 1990.Google Scholar