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Full-Text Articles in Physical Sciences and Mathematics
Supersonic Euler And Magnetohydrodynamic Flow Past Cones, Ian C. Holloway
Supersonic Euler And Magnetohydrodynamic Flow Past Cones, Ian C. Holloway
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This work contains the derivation and type analysis of the conical Euler and Ideal Magnetohydrodynamic equations. The 3 dimensional Euler equations and the Ideal MHD equations with Powell source terms, subject to the assumption that the solution is conically invariant, are projected onto a unit sphere using tools from tensor calculus. Conical flows provide valuable insight into supersonic and hypersonic flow past bodies, but are simpler to analyze and solve numerically. Previously, work has been done on conical inviscid flows governed by the compressible Euler equations with great success. It is known that some flight regimes involve flows of ionized …
Efficient Numerical Methods For Chemotaxis And Plasma Modulation Instability Studies, Truong B. Nguyen
Efficient Numerical Methods For Chemotaxis And Plasma Modulation Instability Studies, Truong B. Nguyen
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In this thesis, we develop efficient numerical solvers for nonlinear systems of partial differential equations (PDEs). These systems of PDEs concern two different sets of physical problems. The first set includes chemotaxis models such as Keller-Segel models and cancer cell invasion models. Solutions of these models are observed to experience the blow-up phenomenon or the development of sharp and spiky features. Therefore, efficient and accurate numerical techniques must be employed in order to capture the solutions' behaviors. For this research, we design efficient solvers for these systems in the one and two spatial dimensions. In particular, we plan to apply …