Radiation Boundary Condition and Anisotropy Correction for Finite Difference Solutions of the Helmholtz Equation

“…Nevertheless, dispersion has been largely ignored in practical implementation of artificial boundary conditions for the Euler equations of gas dynamics [5,7,25]. While boundary conditions that account for the dispersive effects of discretization have been developed in some special cases [3,24], there is no general formulation for linear hyperbolic systems such as the linearized Euler equations.…”

Section: Introductionmentioning

confidence: 99%

Discretely Nonreflecting Boundary Conditions for Linear Hyperbolic Systems

Rowley¹,

Colonius²

2000

Journal of Computational Physics

View full text Add to dashboard Cite

Many compressible flow and aeroacoustic computations rely on accurate nonreflecting or radiation boundary conditions. When the equations and boundary conditions are discretized using a finite-difference scheme, the dispersive nature of the discretized equations can lead to spurious numerical reflections not seen in the continuous boundary value problem. Here we construct discretely nonreflecting boundary conditions, which account for the particular finite-difference scheme used, and are designed to minimize these spurious numerical reflections. Stable boundary conditions that are local and nonreflecting to arbitrarily high order of accuracy are obtained, and test cases are presented for the linearized Euler equations. For the cases presented, reflections for a pressure pulse leaving the boundary are reduced by up to two orders of magnitude over typical ad hoc closures, and for a vorticity pulse, reflections are reduced by up to four orders of magnitude.

show abstract

“…Again the exact solution cannot be obtained; hence, we cannot make a quantitative evaluation of the results and the qualitative evaluation will demonstrate the correctitude of our results. The proposed approach is solved using the Navier-Stokes equations, where the wall boundary conditions and piston source characteristics for wall-embedded pistons, Equations (15)- (16), and the outflow boundary conditions are handled using the PML and acoustic radiation conditions of Tam and Webb [23], Equations (16) and (18). Next, we study the interference of the waves of three sources when the source is characterized by low frequency (ka = 2) and high frequency (ka = 8).…”

Section: Array Of Baffled Pistonsmentioning

confidence: 99%

“…For outflow boundary, we use PML, given by (16) that is finished with the outflow boundary condition designed by Tam and Webb [23] (Equation (18)). …”

Section: Two-dimensional Nonlinear Baffled Pistonmentioning

confidence: 99%

See 1 more Smart Citation

A finite volume‐based high‐order, Cartesian cut‐cell method for wave propagation

Popescu

Vedder

Shyy

2008

Numerical Methods in Fluids

View full text Add to dashboard Cite

SUMMARYComputational aeroacoustics requires numerical techniques capable of yielding low artificial dispersion and dissipation to preserve the amplitude and the frequency characteristics of the physical processes. Furthermore, for engineering applications, the techniques need to handle irregular geometries associated with realistic configurations. We address these issues by developing an optimized prefactored compact finite volume (OPC-fv) scheme along with a Cartesian cut-cell technique. The OPC-fv scheme seeks to minimize numerical dispersion and dissipation while satisfying the conservation laws. The cut-cell approach treats irregularly shaped boundaries using divide-and-merge procedures for the Cartesian cells while maintaining a desirable level of accuracy. We assess these techniques using several canonical test problems, involving different levels of physical and geometric complexities. Richardson extrapolation is an effective tool for evaluating solutions of no high gradients or discontinuities, and is used to evaluate the performance of the solution technique. It is demonstrated that while the cut-cell method has a modest effect on the order of accuracy, it is a robust method. The combined OPC-fv scheme and the Cartesian cut-cell technique offer good accuracy as well as geometric flexibility.

show abstract

Radiation Boundary Condition and Anisotropy Correction for Finite Difference Solutions of the Helmholtz Equation

Cited by 34 publications

References 5 publications

Analytical study of the effect of wave number on the performance of local absorbing boundary conditions for acoustic scattering

Analytical study of the effect of wave number on the performance of local absorbing boundary conditions for acoustic scattering

Discretely Nonreflecting Boundary Conditions for Linear Hyperbolic Systems

A finite volume‐based high‐order, Cartesian cut‐cell method for wave propagation

Contact Info

Product

Resources

About