Course Outline for the Masters Programme in Computational Engineering

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Course Outline for the Masters Programme in Computational Engineering

Compulsory Courses

Course Code Course Title Credit Hours

CP-501 Mathematical Methods for Computational Engineering-I

3 CP-502 Mathematical Methods for Computational

Engineering-II

3 CP-503 Programming and Parallel Processing Tools 3

CP-504 Computer Aided Simulation Techniques 3

CP-505 Finite Element Method 3

Elective Courses- Specialization in Mechanics of Materials

CP-510 Computational Mechanics of Materials 3 CP-511 Numerical Methods for Vibration Analysis 3 CP-512 Multi-body Dynamics Modeling & Simulation 3

CP-513 Continuum Mechanics 3

CP-514 Multiscale Modeling & Simulation of Materials 3 CP-515 Advanced Computational Mechanics of Structures 3

CP-516 Computational Materials Engineering 3

CP-517 Computational Modeling of Composites 3

CP-518 Advanced Materials and Smart Structures 3 *MT-534 Statistical Methods and Data Analysis 3 CP-524 Multi-Physics Modeling and Simulation 3

CP-509 Optimization Methods 3

CP-600 Independent Study Project 6

CP-601 Dissertation 9

*Already approved Course

Elective Courses- Specialization in Thermo and Fluid Dynamics

CP-520 Computational Fluid Dynamics-I 3

CP-521 Computational Fluid Dynamics-II 3

CP-522 Computational Thermodynamics 3

*ME-552 Turbulence Modeling 3

CP-523 Turbo-machine Modeling and Simulation 3 CP-524 Multi-Physics Modeling and Simulation 3

CP-525 Numerical Heat Transfer 3

CP-526 Fuel Cell Modeling & Simulation 3

CP-533 IC Engine Modeling & Simulation 3

*ME-548 Advanced Fluid Mechanics 3

*MT-534 Statistical Methods and Data Analysis 3

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Elective Courses- Specialization in Automotive Engineering

CP-430 Automotive Systems NC

CP-531 Vehicle Kinematic Analysis & Simulation 3

*AU-521 Vehicle Aerodynamics 3

CP-520 Computational Fluid Dynamics-I 3

CP-521 Computational Fluid Dynamics-II 3

*ME-552 Turbulence Modeling 3

CP-532 Vehicle Development Process Tools 3

CP-533 IC Engine Modeling & Simulation 3

CP-534 Vehicle Dynamics 3

CP-535 Vehicle Driveline Simulation 3

CP-524 Multi-Physics Modeling and Simulation 3

*MT-534 Statistical Methods and Data Analysis 3

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Detailed Contents of Courses for the Masters Programme in Computational Engineering

CP-505 Finite Element Method

Fundamentals of finite elements, variational and weighted residual methods; Applications to trusses, beams, plane frames, plane stress and strain problems, axi-symmetric and three-dimensional solids; higher order and isoparametric elements; Applications to field and time-dependent problems of fluid and heat flow; Case studies using commercial software; programming the finite element method.

CP-503 Programming & Parallel Processing Tools

Programming for computation: Variables, Conditional Execution, Loops, Functions, Object-oriented Programming, Inheritance, Virtual Functions, Abstract Base Classes, Templates, Containers, File I/O, Floating Point Numbers, Error Propagation/Analysis, Direct Solution of Linear Equation Systems, Interpolation, Numerical Differentiation and Integration.

Parallel Computing tools: Computer performance and requirements, Computer evolution: scalar, vector, parallel; Memory hierarchy, Data caches, Memory access patterns, Motivation for parallelism, Finding parallelism, Speed-up, Amdahl's law, Taxonomy of parallel computers, Interconnects, Commercial parallel computers, Supercomputing initiatives and future.

Parallel Processing: Shared and Distributed Memory Architectures, Fundamental Algorithms for Shared and Distributed Machines, Parallel Programming Models (MPI tools), Numerical Simulation on High Performance Computing (HPC) Architectures.

CP-501 Mathematical Methods for Computational Engineering-I Applied Linear Algebra

Special Matrices: Stiffness matrix, Tri-diagonal matrix, Circulant or Periodic matrix, Positive definite matrices; solving linear system of equations, Eigen values and Eigen vectors, Inverses and delta functions, Orthogonality and Diagonalization.

Framework of Differential Equation in Engineering

Spring-mass system, Oscillation by Newton’s law, Trusses in equilibrium, Graph Models and Kirchhoff’s laws, Boundary conditions in engineering problems. Least squares for rectangular matrices.

Boundary Value Problems

Classification of differential equations, Differential Equations and Finite elements: Point loads and delta functions, General and weak formulation, quadratic and cubic elements; Gradients and divergence, Laplace’s equation, Fast Poisson’s solver.

Fourier series and Integrals

Fourier series for periodic functions, Discrete Fourier series, Fast Fourier transforms, Convolution and deconvolution, Filtering, Fourier Integral transforms.

CP-502 Mathematical Methods for Computational Engineering-II Initial Value Problems

Heat Equation, Wave equation, Convection-diffusion equation, Accuracy, stability and convergence in finite difference formulations, Diffusion, dissipation and dispersion in numerical solutions, Non-linear Conservation laws in differential and integral forms.

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Solution of Large Linear Systems

Direct elimination methods with reordering; Iterative Methods and Preconditioning: Simple Iteration (Jacobi, Gauss-Seidel, and Incomplete LU), Krylov Methods, Conjugate Gradients and Minimum Residual methods, Multigrid Methods; Inverse Problems and Regularization. Optimization and Minimum Principles

Least square minimization: weighted least squares, minimizing with constraints, saddle points; Calculus of variation, Errors in projections and Eigen values, Linear programming with duality.

CP-504 Computer Aided Simulation Techniques Modelling Techniques in CAD

Basic Geometrical entities (points, curves, surfaces and volumes), Geometrical Interfaces and its constraints, Bottom-up and Top-down approaches in geometric modeling, Parametric Modelling, Geometrical Transformations (Rotation, Translation, Reflection, Scaling, Stretching and Shearing), Geometric symmetries, Geometry Modification and Repair, Import/Export of Geometric models, File structuring of geometric model.

Methods for Meshing

Mesh types (Structured/Unstructured), Mesh Elements (Triangular, Hexahedral, Prismatic), Hybrid Meshing, Mesh refinement, Mesh transformations, Meshing topologies, Surface Meshing Techniques, Volume Meshing Techniques, Adaptive Meshing, Import/Export of Meshing, Mesh-free methods.

Pre- Processing

Domain and sub-domain (domains: solid, fluid, porous etc.) specification, Domain Interfacing, Specifying Boundary and Initial Conditions, Specifying Material and reference properties, Choosing right governing equations/models, Specification of Source Terms in the model.

Processing

Selection of Solvers (2d, 3d, transient, multi-grid, coupled-uncoupled, linear and non-linear, parallel processing etc.), Solver Accuracy levels (Residual level, Domain Imbalance level etc.), Monitoring of solution.

Visualization Techniques

Data importing/exporting, Visualization of scalar fields (iso-surface mapping, volume rendering), Visualization of vector fields (Vector plots, particle tracking), multi-attribute data representation, multi-field visualization, Open source and commercial Post processing tools. Relevant case studies and benchmark problems to be solved using available computational tools.

CP-521 Computational Fluid Dynamics-I

Introduction: What is Computational Fluid Dynamics (CFD), CFD Applications, Numerical vs Analytical vs Experimental, Modeling vs Experimentation, Governing equations of fluid dynamics in differential and integral form with fixed and moving control volume, Mathematical classification of Partial Differential Equations (PDE), Physical and Illustrative examples of elliptic, parabolic and hyperbolic PDE.

Basic schemes of discretization: Finite difference method, Finite element method, Finite volume method, Boundary element method, merits and demerits of each method.

Finite Volume Method for diffusion and Convection Problems: Central differencing scheme, Upwind differencing scheme, Power law and Hybrid scheme, QUICK and higher order differencing schemes, Properties of differencing schemes: Conservativeness, Boundedness, Transportiveness, The concept of false diffusion.

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Discretization of the Momentum Equation: Pressure-Velocity coupling in steady flows, Staggered and Collocated grid, Algorithms for Pressure-Velocity Coupling: SIMPLE, SIMPLE-R, SIMPLE-C, PISO.

Discretization of Unsteady State Problems: 1-D unsteady state diffusion problems, implicit, fully explicit and Crank-Nicholson scheme, Transient SIMPLE and PISO algorithms.

Initial and boundary conditions: symmetry, inlet, outlet, open boundary condition, wall, cyclic boundary conditions and its mathematical description for steady and unsteady flows, incompressible flows, compressible flows, subsonic and supersonic flows.

Numerical Solutions: Segregated versus coupled solver methods, residuals and imbalances, Accuracy of numerical schemes, Types of Errors, false diffusion, stability criterion, relaxation methods, Grid Independent study.

Introduction of turbulence and modelling: Turbulence transport equations, and Turbulence models based on Reynolds Average Navier-Stokes equation (RANS), application of different turbulence models.

Relevant case studies and benchmark problems to be solved using available computational tools.

CP-522 Computational Fluid Dynamics-II

Multiphase Modelling: Multiphase flow examples, particle definition and sizes, porous media, transport equations for multiphase flow, constitutive equations for multiphase flow,Characterization of multiphase flows, coupling between a continuous phase and a dispersed phase, Forces on dispersed particles, Selection of computational models for multiphase flow, closure models.

Particle transport modelling: Particle tracking applications, Lagrangian Particle tracking, forces on the particle, Particle transport models (Basic Erosion Model, Spray Breakup Model, Particle Collision Model, Quasi Static Wall Film Model).

Radiation Modelling: Radiative heat transport equations, material properties for radiation, Radiation models (The P-1 model, Rosseland model, Monte Carlo model, Discrete transfer model, Spectral model).

Combustion Modelling: Basics of Combustion, combustion models (Eddy dissipation model, Finite rate chemistry model, Laminar Flamelet model, Burning velocity model, Residual material model).

CFD Solver formulations: Characteristic-based inviscid flux formulations; viscous flux approximations; eigen systems for numerical flux computation; boundary conditions; iterative implicit algorithms for unsteady and steady problems.

Relevant case studies and benchmark problems to be solved using available computational tools.

CP-509 Optimization Methods

Applications of Linear Optimization, Geometry of the linear optimization, simplex Method, Duality theory, Sensitivity analysis, Robust Optimization, Large Scale Optimization, Network flows, Applications of discrete optimization, Branch and bound and cutting planes, Lagrangean methods, Heuristics and approximation algorithms, Dynamic programming, Applications of nonlinear optimization, Optimality conditions and gradient methods, Line searches and Newton's method, Conjugate gradient methods, Affine scaling algorithm, Interior point methods, Semi-definite optimization.

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CP-513 Continuum Mechanics

Vector and Tensor Calculus: Vector algebra, Tensor algebra: dyadic product, product of two tensors, orthogonal tensor, spectral decomposition, polar decomposition, Tensor analysis: scalar, vector and tensor fields, gradient operation, divergence operator, time derivatives, consistent linearization.

Kinematics of deformation and motion: Foundations of kinematics, deformation, strain tensors, strain rates, deformation gradient, stretch, strain, rotation, shear, rigid motion, local and global length, area and volume changes, principal strains and principal directions, strain deviators, material and spatial time derivatives, vorticity, transport theorems, circulation. Stress Analysis: Surface and body forces, traction and stress, Cauchy theorems, normal and shear stress, hydrostatic and deviatoric stress, principal stresses, Piola- Kirchhoff stress. Field Equations: Conservation of mass, balance of linear and angular momenta, balance of energy, principle of virtual work, entropy inequality.

Constitutive Equations: Material symmetry (isotropy); Hookean solids and Newtonian fluids, Nonlinear Elastic Materials, Covariance, Hyper-elastic materials, constrained materials, Hypo-elastic materials, three-dimensional material laws for visco-elasticity, plasticity, damage; material stability of microstructures.

CP-534 Vehicle Dynamics

Fundamentals of vehicle dynamics, simple longitudinal, lateral and vertical motions.

Vehicle Models and simulations; mechanical modeling and mathematical description of vehicle systems; Infrastructure Models; Vehicle superstructures, Models for support and guidance systems, Models for Vehicle track system.

Occupant protection systems in vehicles, industrial practices, airbags and belt restraint systems along with modeling and simulation of these systems.