Numerical methods for hypersonic boundary layer stability
Journal of Computational Physics
Direct numerical simulation of transition and turbulence in a spatially evolving boundary layer
Journal of Computational Physics
SIAM Journal on Numerical Analysis
Efficient implementation of weighted ENO schemes
Journal of Computational Physics
A high-resolution hybrid compact-ENO scheme for shock-turbulence interaction problems
Journal of Computational Physics
Immersed Interface Methods for Stokes Flow with Elastic Boundaries or Surface Tension
SIAM Journal on Scientific Computing
A Fast Iterative Algorithm for Elliptic Interface Problems
SIAM Journal on Numerical Analysis
Journal of Computational Physics
A family of high order finite difference schemes with good spectral resolution
Journal of Computational Physics
A Cartesian grid embedded boundary method for Poisson's equation on irregular domains
Journal of Computational Physics
Computation of solid-liquid phase fronts in the sharp interface limit on fixed grids
Journal of Computational Physics
The ghost fluid method for deflagration and detonation discontinuities
Journal of Computational Physics
SIAM Journal on Numerical Analysis
A Cartesian grid embedded boundary method for the heat equation on irregular domains
Journal of Computational Physics
A sharp interface Cartesian Ggid method for simulating flows with complex moving boundaries: 345
Journal of Computational Physics
Immersed Interface Methods for Neumann and Related Problems in Two and Three Dimensions
SIAM Journal on Scientific Computing
Three-dimensional elliptic solvers for interface problems and applications
Journal of Computational Physics
Solving a Nonlinear Problem in Magneto-Rheological Fluids Using the Immersed Interface Method
Journal of Scientific Computing
SIAM Journal on Scientific Computing
An Immersed Interface Method for Incompressible Navier-Stokes Equations
SIAM Journal on Scientific Computing
New Geometric Immersed Interface Multigrid Solvers
SIAM Journal on Scientific Computing
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Laminar-turbulent transition of hypersonic boundary layers can be affected significantly by the existence of surface roughness. Currently many important mechanisms of roughness-induced transition are not well understood. In recent years, direct numerical simulation (DNS) has been extensively applied for investigating instability and transition mechanisms of hypersonic boundary layers. Most of the past DNS studies, however, have been based on body-fitted grids for smooth surfaces without roughness. Due to complex geometry of embedded roughness, the use of body-fitted grids can be very difficult for flow with arbitrary surface roughness. In this paper, we present a new high-order cut-cell method to overcome the natural complexities in grid generation around arbitrary surface of roughness. The new method combines a non-uniform-grid finite-difference method for discrete grid points near the solid boundary and a shock-fitting method for the treatment of the bow shock. The non-uniform-grid finite-difference formulas are expressed in a general explicit form so that they can be applied to different multi-dimensional problems without any modification. The computational accuracy of new algorithms of up to O(h^4) are tested on several one- and two-dimensional elliptic equations in irregular domains. In addition, the new method is applied to the simulation of the receptivity process of a Mach 5.92 flow over a flat plate under the combined effect of an isolated surface roughness element and surface blow and suction. A good agreement is found between the unsteady flow results and those obtained by a Linear Stability Theory (LST).