Abstract or Additional Information
ABSTRACT: Solving the linear systems that arise at each time step in an incompressible flow simulation is a very difficult problem. Direct solvers break down for even small problems in 3D, and iterative methods often require sophisticated and expensive preconditioners in order to converge. Over the years, many work-arounds have been developed, to solve instead similar systems, sacrificing accuracy for an ability to efficiently solve the linear systems. We will discuss a class of such work-arounds called algebraic splitting methods, which are widely used in cardiovascular simulations. These methods perform a splitting after building the system matrix, and when done the right way, allow for efficient and robust linear solves without the creation of significant error. We will discuss the implementation and analysis of the methods, and show how the analysis leads to a simple change that results in a full order of accuracy. Several numerical tests are given, and extension to MHD and even steady Navier-Stokes problems are discussed.
HOST: Bill Layton