[CFD] 연재 계획

Contents

• Brief introduction of CFD
• Classification of PDEs
  • 2nd-order linder PDE (parabolic/elliptic/hyperbolic)
  • Systems of equations, Initial and Boundary conditions
• Basics of discretization
  • Basic spatial-/temporal- discretization (FDM, FVM, FEM / explicit, implicit)
  • Finite difference approximations
• Linear stability
  • Concept of stability
  • Modified equation, Numerical dissiapation and dispersion
  • Linear stability analysis, Von Neumann stability, CFL condition
  • Relationship among consistency, stability and convergence
• Model equation of parabolic PDE: Heat equation
  • Basic explicit and implicit schemes
  • Stability analysis
  • Multi-dimensional cases, Fractional step method, ADI scheme, AF-ADI scheme
• Model equation of elliptic PDE: Laplace equation
  • Matrix inversion problem, Direct method, Inversion of tri-diagonal matrix
  • Iteration (relaxation) method, Basic convergence and stability analysis, Jacobi method, Gauss-Seidel method
  • Over-relaxation method, Multigrid method
• Model equation of hyperbolic PDE: Advection equation
  • Basic theory of scalar conservation law, Finite volume discretization, Conservative scheme
  • Lax-Friedrich scheme, Upwind scheme, Lax-Wendroff scheme, MacCormack scheme, Beam-Warming scheme, Crank-Nicolson scheme
  • Time integation method (Multi-step method, Mutli-stage Runge-Kutta method)
  • Gibbs's phenomenon, Godunov's order barrier theorem on monotonicity
  • Non-linear scheme, Concept of total variation