33933 - Computational Thermo-Fluid Dynamics M

Course Unit Page

Academic Year 2018/2019

Learning outcomes

The course deals with the methods for the numerical solution of the balance equations linked to the mass, momentum and energy conservation. A series of CFD commercial software is presented in order to show in which way CFD can help mechanical engineers.

Course contents

PART 1 (Modelling and heat conduction)

Modelling of physical systems. Flux of a physical quantity. Diffusion. Fick's law. Convection. Balance equations. Continuum hypothesis. Generalized balance of a physical quantity. Continuity equation. Momentum balance equation. Energy balance equation. Pressure. Newtonian fluids. Viscous terms. Tensorial expression of the balance equations.

Dimensional analysis and Buckingham's theorem. Dimensionless groups. Dimensionless expression of thermo fluid-dynamics equations. Boussinesq hypothesis. Reynolds number, Grashof number, Prandtl number and their physical meaning. Dynamic and thermal boundary layer Scaling laws for boundary layers. Nusselt number. Dynamic boundary conditions: slip and no-slip condition at the walls. Knudsen number. Thermal boundary conditions: I, II and III kind. Examples. One-way and two-way coordinates. Elliptical, parabolical and hyperbolic problems. Discretization Equations.

Heat conduction with heat generation. Discretization equations deducted by means of the Control Volume Method. Rules about the coefficients of the discretization equations. Dependence on temperature of thermal conductivity. Source term treatment. Metods for the solution of linear algebraic equation systems. Numerical examples. Unsteady heat conduction. Implicit, explicit and Crank-Nicolson methods. Differences among the approaches. Stability conditions. 2D and 3D problems. Gauss-Seidel point-by-point and line-by-line methods. Over-relaxation and under-relaxation.

Monte-Carlo method and heat conduction. Fixed random walk method. Probabilistic interpretation of the discretization equations. 2D steady state heat conduction in presence of a heat source. Effective random walk temperature. Floating random walk method. I, II III kind boundary conditions: treatment of the particles at the boundary of the domain.

PART 2 (Convection)

Continuity equation: its discretization for incompressible fluids with finite volumes and finite differences.
Navier-Stokes equations. Different time discretization schemes: first-order and second-order forward scheme, the leapfrog scheme. Spatial discretization on two-dimensional Cartesian staggered grids: the viscous and convective terms. Centered scheme, first-order upwind, QUICK.
Poisson's equation for the pressure field.


A Pdf version of the complete set of slides used during the course are available.

Teaching methods

Each lesson (in Italian) covers both theoretical and practical aspects. At least, one numerical example is shown for each topic.

Lessons are made by using slides (powerpoint).

Assessment methods

The exam is based on an oral test.

Teaching tools

Lessons are made by using slides (powerpoint).

A pdf copy of the slides (in Italian) is available for UNIBO students at AMS.

Office hours

See the website of Gian Luca Morini

See the website of Beatrice Pulvirenti