Kenneth O. Morgan

The development of an hp -adaptive finite element procedure for electromagnetic scattering problems

The development of an hp-adaptive edge element procedure for the simulation of two-dimensional electromagnetic scattering problems on hybrid meshes of triangles and quadrilaterals is described. The interest in this paper is the accurate prediction of the scattering width for simulations involving a single frequency incident wave. Sharp, constant free, error bounds on the scattering width output are obtained by employing an a posteriori procedure. The elemental contributions to the bound gap are used to drive an adaptive solution process, with the aim of improving the accuracy of the computed output. A novel extension to previous work, is the proposed reduced-order model for the economical calculation of the bound gap for all viewing angles of the scattering width. The theory is supported by numerical examples. This paper constitutes the full length version of the paper that was originally submitted in an extended abstract form for the 2002 Robert J. Melosh medal competition for the best student paper on finite element analysis.

A High Order Finite Volume -HLLC Solver and Anisotropic Delaunay Mesh Adaptation

A high order HLLC Riemann solver is implemented within a finite volume procedure for solving the Euler equations on unstructured grids. The traditional HLLC form is modified slightly to ensure satisfactory performance on stretched meshes and an appropriate limiter is employed to ensure stability and robustness. A Delaunay anisotropic mesh adaptation strategy is introduced with the objective of improving solution accuracy with an optimum number of mesh points, a suitable points inserting algorithm is proposed as well as a Delaunay kernel modification. The electiveness of the proposed approach is demonstrated by application to a number of test examples and the results produced are compared with experiment.

Comparison of Two Explicit Time Domain Unstructured Mesh Algorithms for Computational Electromagnetics

An explicit finite element time domain method and a co-volume approach, based upon a generalization of the well-known finite difference time domain scheme of Yee to unstructured meshes, are employed for the solution of Maxwell’s curl equations in the time domain. A stitching method is employed to produce meshes that are suitable for use with a co-volume algorithm. Examples, involving EM wave propagation and scattering, are included and the numerical performance of the two techniques is compared.

A Parallel Finite Volume Method for Aerodynamic Flows

The solution of 3D transient aerodynamic flows of practical interest is obtained by a finite volume approach, implemented on unstructured tetrahedral and unstructured hybrid meshes. The time discretised equation systems are solved by explicit iteration coupled with multigrid acceleration and the procedure is parallelised for improved computational performance. The examples presented involve an inviscid simulation of store release from a complete aircraft configuration and a viscous simulation of flow over an oscillating wing.

Time Domain Electromagnetic Scattering Simulations on Unstructured Grids

An efficient solution procedure, simulating the interaction between plane electromagnetic waves and electrically large obstacles, is presented. The solution of Maxwell’s curl equations is sought in the time domain by explicit timestepping. The spatial domain is discretised into a mesh of linear tetrahedral elements. To enhance the efficiency of the resulting computational procedure, an edge based representation of the mesh is employed. The Maxwell equations are spatially discretised using a Galerkin method, with stabilisation achieved by the adoption of a Lax-Wendroff numerical flux function. Approaches enabling the accurate modelling of electromagnetic scattering effects over a wide frequency range are investigated, highlighting the significance of the treatment of the mass matrix within the formulation presented. The development of a parallel environment, incorporating parallel mesh generation and parallel solution procedures is also discussed.