High-Order Central ENO Finite-Volume Scheme with Adaptive Mesh Refinement, Paper 2007-4323

A high-order central essentially non-oscillatory (CENO) finite-volume scheme in com-bination with a block-based adaptive mesh refinement (AMR) algorithm is proposed for solution of hyperbolic systems of conservation laws on body-fitted multi-block mesh. The CENO scheme 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 algo-rithm. Switching in the hybrid procedure is determined by a solution smoothness indicator that indicates whether or not the solution is resolved on the computational mesh. The hybrid approach avoids the complexity associated with other ENO schemes that require reconstruction on multiple stencils which in some cases can produce poorly conditioned coefficient matrices. A novel h-refinement criterion based on the solution smoothness in-dicator is used to direct the refinement of the AMR mesh. The predictive capabilities of the proposed high-order AMR scheme are demonstrated for the Euler equations govern-ing two-dimensional compressible gaseous flows. 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 until the desired resolution is achieved is also demonstrated. I