Combinatorial enumeration of groups, graphs, and chemical compounds
Combinatorial enumeration of groups, graphs, and chemical compounds
Non-oscillatory central differencing for hyperbolic conservation laws
Journal of Computational Physics
Three-dimensional adaptive mesh refinement for hyperbolic conservation laws
SIAM Journal on Scientific Computing
Nonoscillatory Central Schemes for Multidimensional Hyperbolic Conservation Laws
SIAM Journal on Scientific Computing
Applied Numerical Mathematics
A Fourth-Order Central WENO Scheme for Multidimensional Hyperbolic Systems of Conservation Laws
SIAM Journal on Scientific Computing
Journal of Scientific Computing
H-Box Methods for the Approximation of Hyperbolic Conservation Laws on Irregular Grids
SIAM Journal on Numerical Analysis
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Central schemes are frequently used for incompressible and compressible flow calculations. The present paper is the first in a forthcoming series where a new approach to a 2nd order accurate Finite Volume scheme operating on Cartesian grids is discussed. Here we start with an adaptively refined Cartesian primal grid in 3D and present a construction technique for the staggered dual grid based on L^~-Voronoi cells. The local refinement constellation on the primal grid leads to a finite number of uniquely defined local patterns on a primal cell. Assembling adjacent local patterns forms the dual grid. All local patterns can be analysed in advance. Later, running the numerical scheme on staggered grids, all necessary geometric information can instantly be retrieved from lookup-tables. The new scheme is compared to established ones in terms of algorithmic complexity and computational effort.