The aim of the course is to present a theoretical analysis and application of basic numerical methods of approximate solution of the differential equations of Transport Phenomena with computers, with the ultimate goal of investigating and revealing the physical content of the predictive mathematical models of the problems. Course content includes: Discretization of boundary value problems. The method of Galerkin weighted residuals. Finite Element basis functions. Discretized Equations. Nonlinear Equations. Computer implementation of the Finite Element Method. Application of Computational Fluid Dynamics methods and codes for the solution of complex Transport Phenomena problems.
- Teacher: Μιχαήλ Καβουσανάκης
- Teacher: Αθανάσιος Παπαθανασίου
ECTS : 3
Language : el
Learning Outcomes : Upon successful completion of the course, the student will be able to possess: • The basic understanding of the approximate solution of a mathematical problem formulated as differential equations and originating from Transport Phenomena. Specifically, the basic understanding of the transition from a differential equation or, more generally, a boundary value problem, to a system of algebraic equations. • The understanding of the theoretical basis of the approximate solution methods for differential equations with emphasis on the finite element method in combination with the Galerkin weighted residuals method. • The understanding of basic concepts: computational mesh/nodes, computational error, convergence, reliability control of approximate solutions. • The understanding of the locality characteristics of the Galerkin/finite element method and the resulting advantages of the method in terms of computational cost of solving the final problem. • The practical understanding of the application of the method through the development of source computational codes in Fortran or Matlab. • The systematic scaling of the implementation of computational analysis by encoding it from one-dimensional linear problems to two-dimensional and nonlinear. • The understanding, with application in computational practice, of the parametric analysis of nonlinear problems. • The training of students in the use of commercial computational fluid dynamics code, Comsol Multiphysics, where complex transport phenomena problems are formulated and solved. The great capabilities of the commercial code in the graphical representation of the solution contribute significantly to the understanding of the physics of the problems. • The understanding of the interaction of transport phenomena as well as physical and geometric parameters of the problems through systematic parametric investigation. Desired skills of students after completing the course: • Self-confidence, ease, and prudence in the use of computational methods. • Ability to control the well-posedness of mathematical problems as models of a physical problem. • Ability to control the reliability of approximate solutions. • Ability to build source computational codes that are sufficiently structured and flexible so that they can be used in a wide range of problems. • Ability to deal with complex geometries and nonlinearities of problems. • Fluency in the use, in as non-superficial a way as possible, of commercial computational codes.