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Examines numerical discretization of the inviscid compressible equations of fluid dynamics; finite-difference and finite-volume methods; time integration, iterative methods, and explicit and implicit algorithms; consistency, stability, error analysis, and properties of numerical schemes, grid generation; and applications to the numerical solution of model equations and the 2D Euler equations. Offered: W.
Student learning goals
Students will be able to determine the mathematical type of the governing equations typically used in CFD and know the appropriate class of computational algorithms.
Students will know a variety of computational algorithms for solving hyperbolic, parabolic, and elliptic partial differential equations relevant to fluid dynamics.
Students will be able to analyze computational algorithms to determine accuracy, convergence, and stability conditions and interpret numerical results within this context.
Students will be able to formulate computational algorithms that can accurately resolve and capture shocks in nonlinear fluid dynamics.
Students will be able to write computer codes to solve the linear advection, nonlinear Burger, and nonlinear Euler equations.
General method of instruction
Lectures, homework assignments, and computer projects
familiarity with computer programming in one or more of the following languages: matlab, python, fortran, c, c++
Class assignments and grading