Research On Hybrid Cell-edge And Cell-node Weighted Compact Nonlinear Schemes And Their Applications

High-resolution schemes have been shown to have lower dispersion anddissipation errors. As a class of numerical tools, they are able to capture themulti-scale features of nonlinear systems, to reduce the demand for grid, and to revealthe evolution process accurately during unsteady simulation. All of these propertieshave resulted in their application to computational aeroacoustics, direct numericalsimulation and large-eddy simulation of turbulent flows. With the increasingrequirements for the accuracy of computation, more and more refined and exactnumerical simulations are needed in application and research fields.The simulation of turbulent compressible flows and shock-boundary layerinteractions requires an algorithm with high accuracy and spectral resolution tocapture different length scales, as well as non-oscillatory behavior acrossdiscontinuities like shock waves. HWCNS scheme has the desired resolutionproperties and thus, with a less stencil width, controllable dissipation and moreexcellent stability, is an ideal candidate for the numerical simulation of such flows.The purpose of this thesis is seeking to construct an algorithm with the non-oscillatorybehavior of the HWCNS scheme as well as the improved spectral resolution andhigher computational efficiency. Such algorithms would be ideal for the simulation offlows where small length scales as well as discontinuities need to be resolvedaccurately. The possibility and feasibility of their application to implicit large-eddysimulation will be explored afterwards.This thesis contains five chapters as follows:Chapter one is the introduction. The development process of high-resolutionschemes in computational fluid dynamics is reviewed, and evolution of HWCNS isdiscussed in detail. Then research on implicit large-eddy simulation using highresolution schemes is introduced. Finally, the current work is described briefly.Chapter two presents the numerical methods used in current thesis. The maincontents include: governing equations, spatial and temporal discretization andboundary conditions.In chapter three, various nonlinear interpolations with high-resolution propertyare discussed. The features of HWCNS are analyzed from three aspects: nonlinearweights, interpolation template and compact evaluation. A weighting strategy withminimum nonlinear-error and moderate computational-cost is chosen throughaccuracy analysis, nonlinear spectrum analysis and numerical tests. Then extension ofinterpolation template form upwind-biased to symmetric is assessed. A compact nonlinear interpolation with high resolution is presented eventually, the new scheme isexplored in terms of nonlinear mechanism, boundary closure and asymptotic stability,characteristic variables. Typical test cases are examined in aspects of convergence rate,computational efficiency, behavior across discontinuities and preserving of flowstructures.In chapter four, the feasibility of applying HWCNS to implicit large-eddysimulation is explored. The discrepancies in RANS simulation are researched firstly:no significant difference in conventional dynamic properties is abserved whilevelocity profiles are only improved with compact interpolation. The HWCNSschemes are then employed in accurate simulation of turbulent flows. The ILEScalculation based on compact nonlinear interpolation shows much superiority withrespect to other calculations. The simulated results of flow around a circular cylinderare in good agreement with experimental or DNS data, so is the behavior within anopen cavity. It is displayed from the velocity spectrum that the original HWCNS istoo dissipative within inertial-range while the improved formulation could reveal thek-5/3law exactly in beneath of the mesh-cut-off frequency.Chapter five reviews all works in this thesis and gives concluding remarks,innovative points and future research directions.Finally, the references and acknowledgements are presented.