Numerical Analysis of Processes

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Code	Completion	Credits	Range	Language
E181141	Z,ZK	4	2P+1C	English

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Department of Process Engineering

Synopsis:

Aim of numerical solutions in structural analysis and computer fluid dynamics. Overview of methods(finite differences, finite volumes, finite elements, boundary elements, meshless methods). Special attention is concentrated to FEM. Model parameter identification - optimisation methods. Examples solved using MATLAB and FLUENT.

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Syllabus of lectures:

1.Aims of numerical methods, databases of literature.

2.Physical models (transport equations, energetic and entropic principles). Empirical models (neural networks and regression models). Analytical solutions (difussion).

Model identification (optimisation).

3.Black box models. Transfer functions. Convolution. Fourier analysis.

4.Nonlinear ODE (Runge Kutta, Adams). Examples: Delay modelling. Strange attractors.

5.ODE / boundary problems. Weighted residual methods. FEM (Finite element method). Examples: Heat exchangers, pipelines. fnite elements in structural analysis (truss, beams, rotationally symmetric shells).

6. PDE classification (hyperbolic, parabolic and elliptic).

Hyperbolic PDE (truss and beams oscillations, elastic pipes and water hammer). MOC (Method Of Characteristics applied to compressible flows).

7. Finite differences (schemes and stability analysis). Hyperbolic equations - water hammer. Parabolic equations - (coffee bean drying).

8. Finite differences. Pulsation flow. Direct ohmic heating. Identification of model parameters by fminsearch.

9. CFD transport equations. Turbulence and RANS models.

10. Finite Volume Method for transport equations. Navier Stokes equations in formulation with primitive variables (method SIMPLE) and formulation using stream-vorticity functions. Laminar cavity flow (FLUENT and MATLAB).

11. Combustion and multiphase flows. Mixture fraction method for nonpremixed combustion. Principles of VOF, Euler-Euler methods for multiphase flows.

12. Multiphase flows in FLUENT

13. Stochastic methods (DPM - Discrete Particles Method)

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