3.00 Credits
Classification of hyperbolic, parabolic, and elliptic partial differential equations (PDEs), types of PDE nonlinearity, method of characteristics, systems of conservation laws, shocks and rarefaction waves; Riemann solutions for linear hyperbolic PDEs; Dynamic solutions for Finite Difference (FD), Finite Volume (FV), and Finite Element Method (FEM); Modal analysis; Time marching schemes: explicit vs. implicit, single- vs. multi-stage, multi-step and sub-cycling, high order schemes; Stability, convergence, and consistency; Physical and numerical dispersion; von Neumann dispersion and dissipation analysis; Adaptivity in space (and time).Cross listed: (Same as: Mechanical Engineering 537.)(DE) Prerequisite(s): Undergraduate level numerical methods and differential equations, or consent of instructor.Recommended Background: Numerical analysis and differential equations.