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1	Results towards a Scalable Multiphase Navier-Stokes Solver for High Reynolds Number Flows Thompson, Travis Brandon 16 December 2013 (has links) The incompressible Navier-Stokes equations have proven formidable for nearly a century. The present difficulties are mathematical and computational in nature; the computational requirements, in particular, are exponentially exacerbated in the presence of high Reynolds number. The issues are further compounded with the introduction of markers or an immiscible fluid intended to be tracked in an ambient high Reynolds number flow; despite the overwhelming pragmatism of problems in this regime, and increasing computational efficacy, even modest problems remain outside the realm of direct approaches. Herein three approaches are presented which embody direct application to problems of this nature. An LES model based on an entropy-viscosity serves to abet the computational resolution requirements imposed by high Reynolds numbers and a one-stage compressive flux, also utilizing an entropy-viscosity, aids in accurate, efficient, conservative transport, free of low order dispersive error, of an immiscible fluid or tracer. Finally, an integral commutator and the theory of anti-dispersive spaces is introduced as a novel theoretical tool for consistency error analysis; in addition the material engenders the construction of error-correction techniques for mass lumping schemes. Navier-Stokes High Reynolds Number Turbulence LES Large Eddy Simulations Entropy Viscosity Entropy-Viscosity Level Set Level Set Method Artificial Compression Artificial Compression Method ACF Compressive Flux Artificial Compressive Flux Integral Commutator Consistency Error Mass Lumping Dispersion Dispersive Error Distersive Error Correction Anti-Dispersive Anti Dispersive

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Results towards a Scalable Multiphase Navier-Stokes Solver for High Reynolds Number Flows