Course Content (Syllabus)
1. Introduction. Error analysis. Essential algorithms for the solution of system of equations. Numerical integration. 2. Linear and non-linear differential equations. Classification of differential equations governing mass transport and heat transfer phenomena. Typical equations governing convection and diffusion problems. The "source term" concept. The importance of boundary conditions and initial conditions. 3. Discretization techniques of differential equations. Taylor expansion. Discretization of first and second order. Error analysis of discretized equations. 4. Finite differences technique. Solution of parabolic, elliptic and hyperbolic flow problems with the use of finite differences technique. Discretization techniques for compressible flow problems. 5. Control volume technique. Numerical integration on a control volume. Control volume techniques adapted for specific problems. The numerical scheme and the interpolation scheme on the control volume technique. The hybrid and the central scheme. Higher order numerical schemes. The SIMPLE and SIMPLEC pressure correction technique. 6. Elements from the grid generation and grid aspects. Classification of grids and grid quality. Transformation from the cartesian to the generalized curvilinear space. Transformation of the fluid flow and heat transfer cartesian equations to the generalized curvilinear forms. The Jacobi determinant. 7. Elements from vector programming. Management of vector units on the computer processor. Programming on a parallel environment for high performance computing. The MPI parallel programming protocol.
CFD, linear and non-linear differential equations, convection, diffusion