Local uniform mesh refinement with moving grids
SIAM Journal on Scientific and Statistical Computing
Local adaptive mesh refinement for shock hydrodynamics
Journal of Computational Physics
An adaptively refined Cartesian mesh solver for the Euler equations
Journal of Computational Physics
An accuracy assessment of Cartesian-mesh approaches for the Euler equations
Journal of Computational Physics
An Adaptive Grid Method and Its Application to Steady Euler Flow Calculations
SIAM Journal on Scientific Computing
Variational Barrier Method of Adaptive Grid Generation in Hyperbolic Problems of Gas Dynamics
SIAM Journal on Numerical Analysis
Adaptive Mesh Methods for One- and Two-Dimensional Hyperbolic Conservation Laws
SIAM Journal on Numerical Analysis
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A nonet-Cartesian grid method, based on anisotropic/isotropic refinement, is presented for solving the Euler equations in gas dynamic problems. Grids are generated automatically, by the recursive subdivision of a single cell into nine subcells for isotropic nonet-Cartesian grids and into three subcells independently in each direction for anisotropic nonet-Cartesian grids, encompassing the entire flow domain. The grid generation method is applied here to steady inviscid shock flow computation. A finite difference formulation for the Euler equation using nonet-Cartesian grids is used to treat complex two-dimensional configuration. Results using this approach are shown to be competitive with other methods. Further, it is demonstrated that this method provides a simple and accurate procedure for solving flow problems involving multielement airfoils.