Second Order Accurate Embedded Boundary Methods for the Solution of PDE’s

Michael Barad, University of California, Davis

The focus of this research is the numerical study of fluid transport in environmental systems. A numerical model is being developed that is based on the variable density incompressible Navier-Stokes equations in 3-D, including air/water and fluid/solid interfaces and the transport of passive constituents. The numerical methodology is based on a second order accurate projection method with higher-order accurate Godunov finite differencing including slope limiters and a stable differencing of the nonlinear convection terms. This is a proven methodology for hyperbolic problems that yields accurate transport with low phase error while minimizing the numerical diffusion at steep gradients typically found in ‘classical’ high order finite difference methods. The approach uses a finite volume discretization, which embeds the geometry within a regular finite difference grid. This finite volume discretization avoids the classic stair-step approximation as is typically found in finite difference methods. For the fast and robust solution of the highly anisotropic elliptic equations in the model a multigrid method is used. Here we give an introduction to our method and present results to date.

Abstract Author(s): Michael Barad