High-Order Solution-Adaptive Central Essentially Non-Oscillatory (CENO) Method for Viscous Flows

摘要: 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 the Navier-Stokes equations on body-fitted multi-block mesh. In contrast to other ENO schemes which require reconstruction multiple stencils, CENO method uses hybrid approach based fixed central stencil. This feature crucial avoiding complexities associated stencils schemes, providing high-order accuracy at relatively lower computational cost as well being very suited extension unstructured meshes. The spatial discretization inviscid (hyperbolic) fluxes combines an unlimited k-exact least-squares technique following from optimal stencil monotonicity-preserving, limited, linear, algorithm. procedure retains cells fully resolved and reverts limited lower-order counterpart under-resolved/discontinuous content. Switching determined by smoothness indicator. viscous (elliptic) are computed same order hyperbolic k-order accurate cell interface gradient derived unlimited, cell-centred, reconstruction. somewhat novel h-refinement criterion indicator used direct steady unsteady adaptation. numerical thoroughly analyzed advection-diffusion problems characterized full range Peclet numbers, its predictive capabilities also demonstrated several laminar flows. ability accurately represent solutions smooth extrema yet robustly handle under-resolved and/or non-smooth content (i.e., shocks discontinuities) shown. Moreover, perform regions demonstrated.