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).

**Lectures**

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

model);

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-

ity);

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

models;

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.

**Practicals**

1. Complex computational continuum mechanics models in action;

2. Numerical linear algebra and High-performance computing.