The student will acquire the theoretical basis of the main numerical methods used in flow simulations. These skills will enable the student to choose among different numerical technologies those best suited to the simulation of a specific engineering problem. Through the use and/or development of numerical solvers, the student will acquire the ability to critically evaluate the results of a numerical simulation.
Solid knowledge of fluid dynamics, physics, and mathematical analysis.
The course includes both theoretical lessons and tutorials to be performed on the computer. The computational tool is used both to deepen the understanding of the theoretical topics and for the development of an assignment. The topic of the assignment can be related to the simulation of real industrial problems, for example, in the field of aerodynamics and internal fluid dynamics, or to the implementation of a numerical algorithm within a CFD solver. The simulation tools necessary for the activities will be made available by the teacher.
The final examination consists of an oral test (lasting approximately 60 minutes), which will be graded on a scale of thirty and includes: 1) the discussion of the project developed during the course (up to 10 points); 2) the presentation and discussion of a theoretical topic (among those of the program) chosen by the candidate (up to 10 points); 3) one or two questions on the theoretical topics covered in the course (up to 10 points).
Governing equations summary; PDEs classification (parabolic, hyperbolic, elliptical); computational domain, boundary and initial conditions; brief introduction to the numerical solution of the governing equations; characteristic form of the compressible Euler equations and its physical interpretation; waves; the Riemann problem; the finite difference method (truncation error, order of accuracy, consistency, higher-order derivatives, mixed-derivatives, approximation of a PDE, implicit and explicit schemes, dissipation and dispersion); numerical stability for marching problems (the round-off error, the Von Neumann Stability Analysis, the Courant-Friederichs-Lewy condition, stability and accuracy: explicit vs. implicit methods); the Finite Volume Method (compressible flows discretization, consistency, local conservation, global conservation, convective fluxes discretization, reconstruction, gradients evaluation, limiters, viscous fluxes discretization); temporal discretization (explicit Runge-Kutta schemes, implicit schemes for steady and unsteady flow problems); incompressible flows discretization (briefly on pressure stabilization techniques, penalty methods and artificial compressibility methods); basics of mesh generation, introduction to turbulence modeling (DNS, RANS, LES).
Non-attending students must contact the lecturer well in advance for the assignment of the examination project.
