An accuracy assessment of Cartesian-mesh approaches for the Euler equations
Journal of Computational Physics
An adaptive Cartesian grid method for unsteady compressible flow in irregular regions
Journal of Computational Physics
Asymptotically stable fourth-order accurate schemes for the diffusion equation on complex shapes
Journal of Computational Physics
The art of computer programming, volume 3: (2nd ed.) sorting and searching
The art of computer programming, volume 3: (2nd ed.) sorting and searching
A higher-order boundary treatment for Cartesian-Grid method
Journal of Computational Physics
A Cartesian grid finite-volume method for the advection-diffusion equation in irregular geometries
Journal of Computational Physics
Difference Approximations for the Second Order Wave Equation
SIAM Journal on Numerical Analysis
H-Box Methods for the Approximation of Hyperbolic Conservation Laws on Irregular Grids
SIAM Journal on Numerical Analysis
Multiresolution Wavelet Based Adaptive Numerical Dissipation Control for High Order Methods
Journal of Scientific Computing
Accurate and stable grid interfaces for finite volume methods
Applied Numerical Mathematics
Difference Approximations of the Neumann Problem for the Second Order Wave Equation
SIAM Journal on Numerical Analysis
A High-Resolution Rotated Grid Method for Conservation Laws with Embedded Geometries
SIAM Journal on Scientific Computing
A Second Order Accurate Embedded Boundary Method for the Wave Equation with Dirichlet Data
SIAM Journal on Scientific Computing
Bounded Error Schemes for the Wave Equation on Complex Domains
Journal of Scientific Computing
A Cartesian grid embedded boundary method for hyperbolic conservation laws
Journal of Computational Physics
Development of low dissipative high order filter schemes for multiscale Navier-Stokes/MHD systems
Journal of Computational Physics
A Simplified $h$-box Method for Embedded Boundary Grids
SIAM Journal on Scientific Computing
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We here generalize the embedded boundary method that was developed for boundary discretizations of the wave equation in second order formulation in Kreiss et al. (SIAM J. Numer. Anal. 40(5):1940---1967, 2002) and for the Euler equations of compressible fluid flow in Sjögreen and Peterson (Commun. Comput. Phys. 2:1199---1219, 2007), to the compressible Navier-Stokes equations. We describe the method and we implement it on a parallel computer. The implementation is tested for accuracy and correctness. The ability of the embedded boundary technique to resolve boundary layers is investigated by computing skin-friction profiles along the surfaces of the embedded objects. The accuracy is assessed by comparing the computed skin-friction profiles with those obtained by a body fitted discretization.