High Order Accuracy Computational Methods For Long Time Integration Of Nonlinear Pdes In Complex Domains

High Order Accuracy Computational Methods for Long Time Integration of Nonlinear PDEs in Complex Domains

High Order Accuracy Computational Methods for Long Time Integration of Nonlinear PDEs in Complex Domains

The overarching goal of this research was to construct stable, robust and efficient high order accurate computational methods for long time integration of nonlinear partial differential equations. High order accuracy methods (Spectral, Finite Difference and Finite Elements) for the numerical simulations of flows with discontinuities, in complex geometries were developed. In particular applications in supersonic combustion were emphasized. Specific research subjects included: Robust high order compact difference schemes, ENO and WENO schemes, discontinuous Galerkin methods, the resolution of the Gibbs phenomenon, parallel computing and high order accurate boundary conditions. In order to overcome the difficulties stemming from complicated geometries, we have developed multidomain techniques as well as spectral methods on arbitrary grids. Several multidimensional codes for supersonic reactive flows had been constructed as well as a library of spectral codes (Pseudopack).

Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2014

The book contains a selection of high quality papers, chosen among the best presentations during the International Conference on Spectral and High-Order Methods (2014), and provides an overview of the depth and breadth of the activities within this important research area. The carefully reviewed selection of papers will provide the reader with a snapshot of the state-of-the-art and help initiate new research directions through the extensive biography.