**Lecturer: Prof. Hrvoje Jasak**

The course objective is to present the formulation, inter-equation coupling and solution procedures for some common multi-physics continuum mechanics problems. The students will:

- understand the formulation and functioning of some common continuum models expressed in terms of partial differential equations, with appropriate closure equations, initial and boundary conditions
- understand the inter-variable coupling and formulation of complex multi-physics systems
- understand various forms of discretisation present in computational continuum mechanics, including Eulerian volumetric (continuum models), lagrangian particle tracking models and Eulerian surface-based models

Upon completion the students will be able to:

- Implement solution procedures for single-physics and multi-physics problems
- Examine and implement coupled discretised models for conjugate and coupled simulations
- Set-up a complete computer simulation of a multi-physics continuum mechanics problem involving multiple solution paradigms (Euler-Lagrange, particle tracking, conjugate heat/mass transfer, solid-fluid interaction)

**Lectures:**

- Modelling of turbulent flows: numerical simulation of turbulent flows, vortex dynamics and energy cascade. Reynolds averaged models: concepts and modelling; eddy viscosity, Reynolds stress transport. Near-wall effects; transitional flows. Large Eddy Simulation; Detached Eddy Simulation. Future of turbulence modelling
- Modelling of compressible and reacting flows: pressure-based algorithms. Compressibility effects, speed of sound, inter-equation coupling. Pressure-velocity-energy coupling in pressure-based solution algorithms. Density-based and pressure-based solvers; block coupled solution. A note on non-equilibrium equation of state (flash boiling model).
- Reacting flow models: modelling framework for reactive flows, Damkohler number), diffusion flames, flamelet model, detailed chemistry modelling. Choice and consequences of modelling paradigms for reacting flows. (Missing: radiation modelling)
- Modelling of multiphase and free surface flows: Euler-Euler multi-phase multi-fluid model and its derived forms.
- 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 compressibility)
- Simulation of nonlinear solid mechanics and fluid-solid interaction. Solidifcation and phase change. Formulation of low-speed solid mechanics models. Linea-r and non-linear governing equations, material and geometric non-linearity. Equation coupling and boundary conditions.
- Discrete phase modelling: Lagrangian particles; discrete element method. Simulation of multi-phase and multi-component flows using Euler-Lagrange models.
- Surface phenomena: Finite Area Method. Model reduction for surface equations: liquid film model

**Practicals**:

- Complex computational continuum mechanics models in action
- Numerical linear algebra and High-performance computing

**Prerequisites:**

Numerical Methods for Incompressible Fluid Dynamics [M12] (E)

**Recommended reading / references:**

- Ferziger, J.H. and Peric, M.: Computational Methods for Fluid Dynamics, Springer Verlag, Berlin-New York, 1995
- Tennekes, Lumley: A First Course in Turbulence, MIT Press 2018
- Marchisio D. and Fox, R.: Multiphase reacting flows: modelling and simulation, Springer 2007