Uniformly high order accurate essentially non-oscillatory schemes, 111
Journal of Computational Physics
On Godunov-type methods for gas dynamics
SIAM Journal on Numerical Analysis
Assessment of Riemann solvers for unsteady one-dimensional inviscid flows for perfect gases
Journal of Computational Physics
Numerical computation of internal & external flows: fundamentals of numerical discretization
Numerical computation of internal & external flows: fundamentals of numerical discretization
Journal of Computational Physics
An adaptively refined Cartesian mesh solver for the Euler equations
Journal of Computational Physics
On essentially non-oscillatory schemes on unstructured meshes: analysis and implementation
Journal of Computational Physics
An accuracy assessment of Cartesian-mesh approaches for the Euler equations
Journal of Computational Physics
Efficient implementation of weighted ENO schemes
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems
SIAM Journal on Numerical Analysis
Weighted essentially non-oscillatory schemes on triangular meshes
Journal of Computational Physics
Journal of Computational Physics
A technique of treating negative weights in WENO schemes
Journal of Computational Physics
Spectral (finite) volume method for conservation laws on unstructured grids: basic formulation
Journal of Computational Physics
A high-order-accurate unstructured mesh finite-volume scheme for the advection-diffusion equation
Journal of Computational Physics
Journal of Scientific Computing
Journal of Computational Physics
Runge--Kutta Discontinuous Galerkin Method Using WENO Limiters
SIAM Journal on Scientific Computing
A fourth-order accurate local refinement method for Poisson's equation
Journal of Computational Physics
Essentially non-oscillatory Residual Distribution schemes for hyperbolic problems
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Spectral Difference Method for Unstructured Grids II: Extension to the Euler Equations
Journal of Scientific Computing
Journal of Computational Physics
A central WENO scheme for solving hyperbolic conservation laws on non-uniform meshes
Journal of Computational Physics
Journal of Computational Physics
Short Note: A limiter for PPM that preserves accuracy at smooth extrema
Journal of Computational Physics
Journal of Computational Physics
Numerical Recipes 3rd Edition: The Art of Scientific Computing
Numerical Recipes 3rd Edition: The Art of Scientific Computing
Time step restrictions for Runge-Kutta discontinuous Galerkin methods on triangular grids
Journal of Computational Physics
International Journal of Computational Fluid Dynamics - CFD 2006 Held at Queens University at Kingston, Ontario, Canada, 1519 July 2006
Journal of Computational Physics
Accuracy preserving limiter for the high-order accurate solution of the Euler equations
Journal of Computational Physics
A Study of Viscous Flux Formulations for a p-Multigrid Spectral Volume Navier Stokes Solver
Journal of Scientific Computing
The Direct Discontinuous Galerkin (DDG) Methods for Diffusion Problems
SIAM Journal on Numerical Analysis
Shock capturing with PDE-based artificial viscosity for DGFEM: Part I. Formulation
Journal of Computational Physics
Local adaptive mesh refinement for shock hydrodynamics
Journal of Computational Physics
On maximum-principle-satisfying high order schemes for scalar conservation laws
Journal of Computational Physics
A parallel solution - adaptive method for three-dimensional turbulent non-premixed combusting flows
Journal of Computational Physics
Journal of Computational Physics
LDG2: A Variant of the LDG Flux Formulation for the Spectral Volume Method
Journal of Scientific Computing
High-order, finite-volume methods in mapped coordinates
Journal of Computational Physics
Self-adjusting, positivity preserving high order schemes for hydrodynamics and magnetohydrodynamics
Journal of Computational Physics
Hi-index | 31.45 |
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 on multiple stencils, the proposed CENO method uses a hybrid reconstruction approach based on a fixed central stencil. This feature is crucial to avoiding the complexities associated with multiple stencils of ENO schemes, providing high-order accuracy at relatively lower computational cost as well as being very well suited for extension to unstructured meshes. The spatial discretization of the inviscid (hyperbolic) fluxes combines an unlimited high-order k-exact least-squares reconstruction technique following from the optimal central stencil with a monotonicity-preserving, limited, linear, reconstruction algorithm. This hybrid reconstruction procedure retains the unlimited high-order k-exact reconstruction for cells in which the solution is fully resolved and reverts to the limited lower-order counterpart for cells with under-resolved/discontinuous solution content. Switching in the hybrid procedure is determined by a smoothness indicator. The high-order viscous (elliptic) fluxes are computed to the same order of accuracy as the hyperbolic fluxes based on a k-order accurate cell interface gradient derived from the unlimited, cell-centred, reconstruction. A somewhat novel h-refinement 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-diffusion problems characterized by the full range of Peclet numbers, and its predictive capabilities are also demonstrated for several inviscid and laminar 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. Moreover, the ability to perform mesh refinement in regions of under-resolved and/or non-smooth solution content is also demonstrated.