## Department of Whole Vehicle Engineering - Audi Hungaria Faculty of Automotive Engineering

Computational Fluid Dynamics

Course Summary

The goal of this course is to make engineering students informed users of Computational Fluid Dynamics (CFD) who can not only run CFD simulations but also fully understand their mathematical background and are able to make conscious choices of the appropriate numerical parameters. To achieve this, the relevant Fluid Mechanics laws, the governing equations as well as the applied numerical methods will be reviewed. Also, students will complete three practically oriented simulation assignments and learn how to present these in written form according to the internationally accepted standards. It is assumed that enrolled students have had at least one Fluid Mechanics course completed at the undergraduate level.

Topics discussed:

• Introduction: Motivation, What is Computational Fluid Dynamics (CFD), Role of CFD in Vehicle Engineering and design

• Governing equations in CFD 1: Review of continuum concept, mass, energy and momentum conservation and derivation of the Navier-Stokes equations

• Governing equations in CFD 2: Flux vector formulation of the N-S equations, Conservative vs. primitive forms, Euler equations, Model equations

• Classification of differential equations: ODE’s vs. PDE’s, Linear vs. non-linear equations, First-order vs. higher-order equations, Conservative vs. non-conservative forms

• Classification of Partial Differential Equations (PDE’s): Determining the nature of PDE’s (elliptic, parabolic, hyperbolic), Physical meaning for fluid flows, Computational meaning for fluid flows, Boundary and initial conditions for PDE’s

• Turbulence 1: Sources and physics of turbulence, Kolmogorov length scale, Differences between turbulence modelling, Large Eddy Simulation (LES) and Detached Eddy Simulation (DES) and Direct Numerical Simulations (DNS). Limitations and applicability.

• Turbulence 2: Free turbulent flows, Boundary layers near solid walls, Turbulence modeling in CFD, Wall functions and implications for grid generation

• Numerical solution of PDE’s: Selection of mathematical model, Selection of discretization method (Finite Difference, Finite Volume, Finite Element, Spectral Method)

• Grid generation: Structured vs. unstructured grids, Grid transformation, Cartesian grids, Zonal or block-structured grids, Hybrid grids, Moving mesh techniques (Sliding mesh, CHIMERA grids) Deforming mesh techniques, Adaptive grids, Multigrid methods and their relation to grid generation, Basic guidelines for grid generation

• Boundary treatment: Boundary conditions, Boundary treatment (Changing the numerical method at edges, Changing the computational domain at edges), Solid Wall boundary treatment, Far-field boundary treatment, Non-reflecting boundaries

• Solution techniques for the discretized equations: Explicit vs. implicit formulations, Solutions techniques for explicit method (Lax-Wendroff, MacCormack, Runge-Kutta), Solution techniques for implicit methods (Direct methods /Gaussian elimination, Cramer’s rule/, Indirect methods /Thomas algorithms, point-iterative methods, approximate factorization/)

• Errors and uncertainty in CFD: Sources of error, Sources of uncertainty, Stability analysis of numerical errors (Discrete Perturbation analysis, Von Neumann Stability Analysis, Multidimensional considerations), The Courant-Friedrich-Loewy number (CFL), Stability vs. accuracy, Local vs. Global time stepping, Evaluation of convergence (Iterations convergence: residuals, Grid convergence, Time step convergence), Characteristic features related to stability (Consistency, Boundedness, Transportiveness)

• Special topics in CFD: specifics of the Finite Volume Method, Riemann solvers, upwinding, higher order methods

• Summary and review

Course administrator - Dr. T. Jakubík - SZE
Instructor - Dr. D. Feszty - AUDI Hungaria Motor Kft.