High-order solution-adaptive central essentially non-oscillatory (CENO) method for viscous flows

A high-order central essentially non-oscillatory (CENO) nite-volume scheme in combination with a block-based adaptive mesh re nement (AMR) algorithm is proposed for solution of the Navier-Stokes equations on bodytted multi-block mesh. The spatial discretization of the inviscid (hyperbolic) term is based on a hybrid solution reconstruction procedure that combines an unlimited high-order k-exact least-squares reconstruction following from a xed central stencil with a monotonicity preserving limited linear reconstruction algorithm. The unlimited k-exact reconstruction is used for cells in which the solution is fully resolved and the limited lower-order counterpart is applied to computational cells with under-resolved/discontinuous solution content. 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 to provide high-order accuracy at lower computational cost and to be very well suited for extension to unstructured meshes. The high-order viscous (elliptic) uxes are computed based on a k-order accurate gradient derived from the same unlimited high-order reconstructions. A somewhat novel h-re nement criterion based on the solution smoothness indicator is used to direct the steady and unsteady mesh adaptation. The proposed numerical procedure is thoroughly analyzed for advection-di usion problems characterized by a full range of P eclet numbers, and its predictive capabilities are demonstrated for several laminar ows. The ability of the scheme to accurately represent solutions with smooth extrema and yet robustly handle under-resolved and/or non-smooth solution content is shown. Moreover, the ability to perform mesh re nement in regions of smooth but under-resolved and/or non-smooth solution content to achieve the desired resolution is also demonstrated.