A high-order central essentially non-oscillatory (CENO) finite-volume scheme in combination with a block-based adaptive mesh refinement (AMR) algorithm is proposed for solution of hyperbolic and elliptic systems of conservation laws on body- fitted multi-block mesh. The spatial discretization of the hyperbolic (inviscid) terms is based on a hybrid solution reconstruction procedure that combines an unlimited high-order k-exact least-squares
reconstruction technique following from a fixed central stencil with a monotonicity preserving limited piecewise linear reconstruction algorithm. The limited reconstruction is applied to computational cells with under-resolved solution content and the unlimited k-exact reconstruction
procedure is used for cells in which the solution is fully resolved. Switching in the
hybrid procedure is determined by a solution smoothness indicator. The hybrid approach
avoids the complexity associated with other ENO schemes that require reconstruction on
multiple stencils and therefore, would seem very well suited for extension to unstructured meshes. The high-order elliptic (viscous) fluxes are computed based on a k-order accurate average gradient derived from a (k+1)-order accurate reconstruction. A novel h-refinement criterion based on the solution smoothness indicator is used to direct the steady and unsteady refinement of the AMR mesh. The predictive capabilities of the proposed high-order AMR scheme are demonstrated for the Euler and Navier-Stokes equations governing two-dimensional
compressible gaseous flows as well as for advection-diffusion problems characterized
by the full range of Peclet numbers, Pe. The ability of the scheme to accurately represent
solutions with smooth extrema and yet robustly handle under-resolved and/or non-smooth solution content (i.e., shocks and other discontinuities) is shown for a range of problems. Moreover, the ability to perform mesh refinement in regions of smooth but under-resolved and/or non-smooth solution content to achieve the desired resolution is also demonstrated.
| Identifer | oai:union.ndltd.org:TORONTO/oai:tspace.library.utoronto.ca:1807/29759 |
| Date | 31 August 2011 |
| Creators | Ivan, Lucian |
| Contributors | Groth, Clinton P. T. |
| Source Sets | University of Toronto |
| Language | en_ca |
| Detected Language | English |
| Type | Thesis |
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