2.29 Numerical Fluid Mechanics, Fall 2011
Numerical Fluid Mechanics
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This course will provide students with an introduction to numerical methods and MATLAB®. Topics covered throughout the course will include: errors, condition numbers and roots of equations; Navier-Stokes; direct and iterative methods for linear systems; finite differences for elliptic, parabolic and hyperbolic equations; Fourier decomposition, error analysis, and stability; high-order and compact finite-differences; finite volume methods; time marching methods; Navier-Stokes solvers; grid generation; finite volumes on complex geometries; finite element methods; spectral methods; boundary element and panel methods; turbulent flows; boundary layers; Lagrangian Coherent Structures. Subject includes a final research project.
errors, condition numbers and roots of equations, Navier-Stokes, direct and iterative methods for linear systems, finite differences for elliptic, parabolic and hyperbolic equations, Fourier decomposition, error analysis, and stability, high-order and compact finite-differences, finite volume methods, time marching methods, Navier-Stokes solvers, grid generation, finite volumes on complex geometries, finite element methods, spectral methods, boundary element and panel methods, turbulent flows, boundary layers, Lagrangian Coherent Structures
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An effective overlapping finite element method : the method of finite spheres for three-dimensional linear elasticity problems Lai, Benjamin, Ph. D. Massachusetts Institute of Technology (Massachusetts Institute of Technology, 2016)The method of finite spheres is an effective overlapping finite element method developed to overcome challenges in mesh-based numerical methods. Commonly recognized challenges include mesh generation for geometrically ...