An analysis of finite-difference and finite-volume formulations of conservation laws
Journal of Computational Physics
Dispersion-relation-preserving finite difference schemes for computational acoustics
Journal of Computational Physics
The stability of numerical boundary treatments for compact high-order finite-difference schemes
Journal of Computational Physics
Several new numerical methods for compressible shear-layer simulations
Applied Numerical Mathematics
Finite Volume Formulation of Compact Upwind and Central Schemes with Artificial Selective Damping
Journal of Scientific Computing
A finite volume formulation of compact central schemes on arbitrary structured grids
Journal of Computational Physics
An implicit compact scheme solver with application to chemically reacting flows
Journal of Computational Physics
A 2D compact fourth-order projection decomposition method
Journal of Computational Physics
Journal of Computational Physics
High-order Compact Schemes for Nonlinear Dispersive Waves
Journal of Scientific Computing
Metric Identities and the Discontinuous Spectral Element Method on Curvilinear Meshes
Journal of Scientific Computing
Journal of Computational Physics
High-order compact finite-difference methods on general overset grids
Journal of Computational Physics
On the use of a high order overlapping grid method for coupling in CFD/CAA
Journal of Computational Physics
Generation of curvilinear coordinates on multiply connected regions with boundary singularities
Journal of Computational Physics
Generalized characteristic interface conditions for high-order multi-block computation
International Journal of Computational Fluid Dynamics
Asymptotic and numerical analysis of an inviscid bounded vortex flow at low Mach number
Journal of Computational Physics
Journal of Computational Physics
Design and analysis of a new filter for LES and DES
Computers and Structures
Journal of Computational Physics
A massively parallel multi-block hybrid compact-WENO scheme for compressible flows
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Curvilinear finite-volume schemes using high-order compact interpolation
Journal of Computational Physics
Journal of Computational and Applied Mathematics
A shock-detecting sensor for filtering of high-order compact finite difference schemes
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Discontinuous Galerkin spectral element approximations on moving meshes
Journal of Computational Physics
High-order, finite-volume methods in mapped coordinates
Journal of Computational Physics
Stabilized non-dissipative approximations of Euler equations in generalized curvilinear coordinates
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
New shock detector for shock-boundary layer interaction
HPCA'09 Proceedings of the Second international conference on High Performance Computing and Applications
Boundary states at reflective moving boundaries
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Grid stabilization of high-order one-sided differencing II: Second-order wave equations
Journal of Computational Physics
A sparse and high-order accurate line-based discontinuous Galerkin method for unstructured meshes
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
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This study enables the use of very high-order finite-difference schemes for the solution of conservation laws on stretched, curvilinear, and deforming meshes. To illustrate these procedures, we focus on up to 6th-order Pade-type spatial discretizations coupled with up to 10th-order low-pass filters. These are combined with explicit and implicit time integration methods to examine wave propagation and wall-bounded flows described by the Navier-Stokes equations. It is shown that without the incorporation of the filter, application of the high-order compact scheme to nonsmooth meshes results in spurious oscillations which inhibit their applicability. Inclusion of the discriminating low-pass high-order filter restores the advantages of high-order approach even in the presence of large grid discontinuities. When three-dimensional curvilinear meshes are employed, the use of standard metric evaluation procedures significantly degrades accuracy since freestream preservation is violated. To overcome this problem, a simple technique is adopted which ensures metric cancellation and thus ensures freestream preservation even on highly distorted curvilinear meshes. For dynamically deforming grids, an effective numerical treatment is described to evaluate expressions containing the time-varying transformation metrics. With these, techniques, metric cancellation is guaranteed regardless of the manner in which grid speeds are defined. The efficacy of the new procedures is demonstrated by solving several model problems as well as by application to flow past a rapidly pitching airfoil and past a flexible panel.