Modeling a no-slip flow boundary with an external force field
Journal of Computational Physics
An adaptively refined Cartesian mesh solver for the Euler equations
Journal of Computational Physics
Krylov methods for the incompressible Navier-Stokes equations
Journal of Computational Physics
Numerical simulation of a cylinder in uniform flow: application of a virtual boundary method
Journal of Computational Physics
An immersed boundary method with formal second-order accuracy and reduced numerical viscosity
Journal of Computational Physics
Second-generation wavelet collocation method for the solution of partial differential equations
Journal of Computational Physics
A ghost-cell immersed boundary method for flow in complex geometry
Journal of Computational Physics
An Adaptive Wavelet Collocation Method for Fluid-Structure Interaction at High Reynolds Numbers
SIAM Journal on Scientific Computing
DNS of buoyancy-dominated turbulent flows on a bluff body using the immersed boundary method
Journal of Computational Physics
Wavelet-Based Adaptive Solvers on Multi-core Architectures for the Simulation of Complex Systems
Euro-Par '09 Proceedings of the 15th International Euro-Par Conference on Parallel Processing
Prediction of wall-pressure fluctuation in turbulent flows with an immersed boundary method
Journal of Computational Physics
Pores resolving simulation of Darcy flows
Journal of Computational Physics
Journal of Computational Physics
On the use of immersed boundary methods for shock/obstacle interactions
Journal of Computational Physics
Shape optimization for drag reduction in linked bodies using evolution strategies
Computers and Structures
Journal of Computational Physics
Finite Element Approximation of Nonsolenoidal, Viscous Flows around Porous and Solid Obstacles
SIAM Journal on Numerical Analysis
SIAM Journal on Scientific Computing
A simple second order cartesian scheme for compressible Euler flows
Journal of Computational Physics
Journal of Computational Physics
An optimal penalty method for a hyperbolic system modeling the edge plasma transport in a tokamak
Journal of Computational Physics
Hi-index | 31.50 |
To simulate flows around solid obstacles of complex geometries, various immersed boundary methods had been developed. Their main advantage is the efficient implementation for stationary or moving solid boundaries of arbitrary complexity on fixed non-body conformal Cartesian grids. The Brinkman penalization method was proposed for incompressible viscous flows by penalizing the momentum equations. Its main idea is to model solid obstacles as porous media with porosity, @f, and viscous permeability approaching zero. It has the pronounced advantages of mathematical proof of error bound, strong convergence, and ease of numerical implementation with the volume penalization technique. In this paper, it is extended to compressible flows. The straightforward extension of penalizing momentum and energy equations using Brinkman penalization with respective normalized viscous, @h, and thermal, @h"T, permeabilities produces unsatisfactory results, mostly due to nonphysical wave transmissions into obstacles, resulting in considerable energy and mass losses in reflected waves. The objective of this paper is to extend the Brinkman penalization technique to compressible flows based on a physically sound mathematical model for compressible flows through porous media. In addition to penalizing momentum and energy equations, the continuity equation for porous media is considered inside obstacles. In this model, the penalized porous region acts as a high impedance medium, resulting in negligible wave transmissions. The asymptotic analysis reveals that the proposed Brinkman penalization technique results in the amplitude and phase errors of order O((@h@f)^1^/^2) and O((@h/@h"T)^1^/^4@f^3^/^4), when the boundary layer within the porous media is respectively resolved or unresolved. The proposed method is tested using 1- and 2-D benchmark problems. The results of direct numerical simulation are in excellent agreement with the analytical solutions. The numerical simulations verify the accuracy and convergence rates.