SBIR Phase I: Highly Accurate Reconstruction Module For Multidisciplinary Computation

This Small Business Innovation Research Phase I project will develop a highly accurate reconstruction module for Godunov-type schemes to upgrade the capability of current multidisciplinary computational software packages for simulation of a class of engineering problems with small scales and high frequencies. The unique and innovative aspect of this work is to combine both Weighted Essentially Non-Oscillatory (WENO) concept and compact differencing into a single upwind algorithm. Instead of using multiple polynomial candidates, a hybrid power-exponential spline is used as the underlying interpolation for a WENO scheme with local smoothness measures as the perturbation parameters. In this way, the weight functions of a WENO scheme can be analytically determined from the underlying interpolation. Their Taylor series expansions around the smooth regions can be used for further accuracy improvement. The resulting piecewise quadratic reconstruction with compact difference computed slope and curvature can dramatically reduce numerical diffusion inherent in upwind schemes. By using this upwind scheme, the numerical simulation of vortex dominated flows, boundary layers, turbulence, acoustic waves, and electromagnetic waves, etc., can be significantly improved without loss of the shock-capturing feature. The highly accurate reconstruction module, which is independent of physics, can be easily integrated into the current production and research codes and has the potential of providing cost improvement of at least an order of magnitude over the current versions.