Thesis / Dissertation

A Framework for Multidimensional Analysis and Development of Numerical Schemes

Yiyun Raynold Tan, Andrew Ooi (ed.)

Published : 2020

Abstract

Partial differential equations are found throughout engineering and sciences. Under the constraint of complex initial and boundary conditions, most of these complex equations do not have analytical solutions, and therefore require solution by numerical methods. In the context of this thesis, the goal is to examine the governing equations of fluid mechanics (Euler and Navier Stokes) which require both spatial and temporal discretization. Under the effects of numerical differencing, the numerical solution is subjected to both dispersion and dissipation error. These error can be identified and analyzed through spectral analysis method. The analysis of numerical schemes under a coupled spatial t..

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