Fundamentals of Computational Fluid Dynamics. In view of the increasing role of Computational Methods in Fluid Mechanics and the advent of advanced commercial software providing numerical solutions to flow problem, this course emphasizes the essential understanding of the mathematics of development and analysis of computer models and (fast) solution methods as well as for the critical evaluation of results in terms of accuracy and physical relevance. After the course the student is able to.
- Distinguish the physical aspects of a flow described by the Navier Stokes equations that are represented by the advection diffusion equation and those represented by the Laplace equation, and understand why these scalar problems are good model problems characterizing the behavior of the full system of the Navier why these model problems represent the character of the entire system of equations.
- Explain the aspects of a flow represented by the advection diffusion equation and those by the Laplace equation as model problems and why these model problems represent the character of the entire system.
- Analyze schemes for discretization of the advection diffusion and Laplace equation in terms of stability and accuracy
- Analyze the performance of numerical solution schemes in terms of stability, and computational efficiency
- Explain and analyze Multigrid/Multilevel computational methods for elliptic problems.
- Solve characteristic linear and nonlinear hyperbolic model equations (Burgers’ equation and 1D Euler equations) and explain the role of artificial dissipation in numerical schemes.
- Design/develop and implement a numerical solution algorithm for a representative hyperbolic or elliptic (system) of equations and provide complete description and explanation of analysis, performance, and results in a technical report.
- Explain and discuss relevant issues of basic CFD solver development
By means of several model problems and characteristic equations the basic knowledge regarding the numerical solution of fluid mechanics problems is taught. Relevant aspects are elliptic and hyperbolic behavior, systems of equations, discretization, accuracy, stability and computational efficiency (Multiscale/Multigrid methods). This knowledge provides the capability to interpret and understand numerical solutions to complex flow problems. The philosophy of this course is that the student will only be able to master these topics by actually doing it himself.