Higher order panel methods are used to solve the Laplace equation in the presence of complex geometries. These methods are useful when globally accurate velocity or potential fields are desired as in the case of vortex based fluid flow solvers. This paper develops a fast multipole algorithm to compute velocity fields due to higher order, two-dimensional vortex panels. The technique is applied to panels having a cubic geometry and a linear distribution of vorticity. The results of the present method are compared with other available techniques. © 2005 Society for Industrial and Applied Mathematics.

M Ramakrishna

Department of Aerospace Engineering

Ramachandran, P.

Surya C. Rajan

FAST MULTIPOLE METHOD

HIGHER ORDER PANELS

PANEL METHOD

VELOCITY FIELDS

Algorithms

Flow of fluids

Laplace transforms

Potential Flow

Problem solving

Velocity measurement

Natural sciences computing

Fulltext

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IIT Madras

A Fast Multipole Method for Higher Order Vortex Panels in Two Dimensions

SIAM Journal on Scientific Computing

Vortex methods offer a grid-free alternative to simulating incompressible, viscous, fluid flows. They require the use of fairly sophisticated algorithms and can be complicated to implement for general flows. This article describes an object-oriented design used to implement a vortex particle based flow solver in two dimensions. We provide an overview of the various abstractions that arose as a result of this design. Several of the algorithms have common components that may be abstracted and reused. We demonstrate how the design allowed us to derive the traditional benefits of OOD. In addition, we show how the design directly suggested elegant generalizations of existing algorithms. Finally, we show the benefits of using software testing techniques and building a powerful scripting layer for the library. © 2009 ACM.

ACM Transactions on Mathematical Software

An object-oriented design for two-dimensional vortex particle methods

A new two-dimensional panel technique has been developed to solve Laplacian flows, which eliminates the edge effect present in traditional panel methods. Such a method is very useful for applications where the velocity induced by the panels is required at arbitrary locations. Particle based flow solvers are a prime example. The method, however, requires considerably more computational effort. In this paper the method is modified to improve computational efficiency by adapting the fast multipole algorithm for the panel method. Significant improvement in computational efficiency is obtained while ensuring that the edge effects are eliminated.

A fast, two-dimensional panel method

Low-Speed Aerodynamics

Journal of Computational Physics

Acceleration of Contour Dynamics Simulations with a Hierarchical-Element Method

Yet Another Fast Multipole Method without Multipoles—Pseudoparticle Multipole Method

SIAM Journal on Scientific and Statistical Computing

An Implementation of the Fast Multipole Method without Multipoles

A fast multipole method for higher order vortex panels in two dimensions

Journal	SIAM Journal on Scientific Computing
ISSN	10648275
Open Access	Yes