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Dr Hrvoje Jasak

Introduction to continuum mechanics models beyond single-phase fluid flow.
Models are expressed as sets of coupled partial differential equations, cover-
ing multi-physics applications. The solution algorithm part of the course will
cover implicit solution methods of sparse linear equation sets in the frame-
work of High-Performance Computing (HPC).


1. Modelling of turbulent flows: numerical simulation of turbulent flows,
vortex dynamics and energy cascade. Reynolds averaged models: con-
cepts and modelling; eddy viscosity, Reynolds stress transport. Near-
wall effects; transitional flows. Large Eddy Simulation; Detached Eddy
Simulation. Future of turbulence modelling;

2. Modelling of compressible and reacting flows: pressure-based algo-
rithms. Compressibility effects, speed of sound, inter-equation cou-
pling. Pressure-velocity-energy coupling in pressure-based solution al-
gorithms. Density-based and pressure-based solvers; block coupled
solution. A note on non-equilibrium equation of state (flash boiling

3. Reacting flow models: modelling framework for reactive flows, Damkohler
number), diffusion flames, flamelet model, detailed chemistry mod-
elling. Choice and consequences of modelling paradigms for reacting
flows. (Missing: radiation modelling);

4. Modelling of multi-phase and free surface flows: Euler-Euler multi-
phase multi-fluid model and its derived forms;

5. Free surface flow model; preserving sharp interface, VOF, level set and
phase field equation. Pressure-velocity-VOF coupling issues; preserving
sharp interface,ghost-fluid method. (Extension to phase compressibil-

6. Simulation of nonlinear solid mechanics and fluid-solid interaction. So-
lidification and phase change. Formulation of low-speed solid mechan-
ics models. Linear and non-linear governing equations, material and
geometric non-linearity. Equation coupling and boundary conditions;

7. Discrete phase modelling: Lagrangian particles; discrete element method.
Simulation of multi-phase and multi-component flows using Euler-Lagrange

8. Surface phenomena: Finite Area Method. Model reduction for surface
equations: liquid film model;

9. Model-to-model interaction and coupling procedure. Volumetric, La-
grangian and surface models. Conjugate and coupled solution. Aspects
of model-to-model coupling, local and global conservation, accuracy
concerns, validation and verification;

10. Unified approach to solid and fluid mechanics modelling: phase change,
solidification and residual stress modelling (low-speed phenomena)Model
development, jump conditions and discontinuities.


1. Complex computational continuum mechanics models in action;
2. Numerical linear algebra and High-performance computing.