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Please use this identifier to cite or link to this item: http://hdl.handle.net/1807/29759

Title: Development of High-order CENO Finite-volume Schemes with Block-based Adaptive Mesh Refinement (AMR)
Authors: Ivan, Lucian
Advisor: Groth, Clinton P. T.
Department: Aerospace Science and Engineering
Keywords: computational fluid dynamics
finite-volume method
high-order scheme
adaptive mesh refinement (AMR)
ENO scheme
essentially non-oscillatory
CENO
body-fitted multi-block mesh
high-order spatial discretization
numerical method
hyperbolic and elliptic PDE
fixed stencil reconstruction
piecewise linear reconstruction
smoothness indicator
Euler and Navier-Stokes equations
advection-diffusion equation
smooth and non-smooth solution content
k-exact least-squares reconstruction
hybrid numerical scheme
compressible gaseous flows
refinement criteria
high-performance parallel computing
solution monotonicity enforcement
large-eddy simulation (LES)
interpolation technique
structured grid
inviscid and viscous flow
TVD scheme
h-p-adaptation
high-order boundary conditions
complex curved geometries
Issue Date: 31-Aug-2011
Abstract: 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.
URI: http://hdl.handle.net/1807/29759
Appears in Collections:Doctoral

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