A modification of the weeks method for numerical inversion of the Laplace transform
Mathematics of Computation
Computer Methods in Applied Mechanics and Engineering
The numerical performance of Tricomi's formula for inverting the Laplace transform
Numerische Mathematik
A finite difference, frequency-domain numerical scheme for the solution of the gust response problem
Journal of Computational Physics
A formulation of asymptotic and exact boundary conditions using local operators
Applied Numerical Mathematics - Special issue on absorbing boundary conditions
Numerical Inversion of Laplace Transforms Using Laguerre Functions
Journal of the ACM (JACM)
Numerical Inversion of Laplace Transforms by Relating Them to the Finite Fourier Cosine Transform
Journal of the ACM (JACM)
Rapid Evaluation of Nonreflecting Boundary Kernels for Time-Domain Wave Propagation
SIAM Journal on Numerical Analysis
An integral evolution formula for the wave equation
Journal of Computational Physics
A potential-theoretic method for far-field sound radiation calculations
Journal of Computational Physics
High-Order Radiation Boundary Conditions for the Convective Wave Equation in Exterior Domains
SIAM Journal on Scientific Computing
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
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This paper introduces a competitive computational approach for determining time-dependent far-field sound generated by subsonic flows around lifting airfoils. The procedure assumes the linearity of the sound field away from a bounded region surrounding the airfoil. It is assumed that the sound pressure on the boundary of this enclosed region (referred to as the Kirchhoff surface) is specified, possibly by another procedure such as solving the full Euler equations. Away from the Kirchhoff surface, the Euler equations are linearized about a uniform mean flow. It is well known that linearized Euler equations can be uncoupled into a scalar convective wave equation. However, due to the anisotropy present in the convective wave equation, it is difficult to compute solutions. In this context, direct numerical simulation of the convective wave equation requires proper numerical descriptions of far-field boundary conditions which is a non-trivial task. Moreover, if accurate far-field conditions can be formulated, the computational cost of direct simulation can be prohibitive even in a modest computational domain. In this paper, we present an alternate solution procedure. First, the problem is transformed via the Laplace transform (with appropriate initial conditions) into a reduced wave equation. The convective term in the reduced wave equation is removed using a dependent variable transformation. Then we use Gothert's rule, to obtain a Helmholtz like equation with complex wave number, which is subsequently solved using double layer potential theory. Finally upon application of numerical inverse Laplace transform techniques, far-field acoustic pressure is obtained as a function of space and time.