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Center for Nonlinear Studies |
Most modern codes for compressible fluid flows use finite volume approximations in which the equations of motion are solved in integral form. If the domain of the integral remains finite (e.g., a computational cell) and the equations are nonlinear, then integral solutions are not exactly equivalent to those of the associated differential form. In this talk, we describe a finite scale analysis that takes into account the finiteness of the computational cell size in estimating numerical error and uncertainty in computer simulations. In particular, we introduce the concept of structure functions, which are unique, continuous solutions of the discrete equations. We show how to derive them theoretically, how to construct them numerically, and how to employ them for generic analysis of numerical algorithms. Tagline: Delta x never goes to zero.
Host: Mikhail Shashkov. shashkov@lanl.gov, 667-4400