AKTU Physical and Numerical Simulation (BMN053) Syllabus PDF – B.Tech 3rd Year

Course Outcome: After the end of the course the student will be able to

1. Students will understand the fundamental concepts and principles underlying both physical and numerical simulation techniques.
2. Students will be able to apply dimensional analysis and understand the methodology and material selection for physical modelling in engineering problems.
3. Students will gain proficiency in the theoretical foundations and application of the Boundary Element Method (BEM), including specific techniques like the displacement-discontinuity method.
4. Students will comprehend the Finite Difference Method (FDM) and its mesh generation, along with the ability to identify and apply both FDM and Finite Element Method (FEM) to solve relevant mining-related problems.

UNIT-1 Introduction to Simulation and Physical Modeling Fundamentals:

Introduction to Simulation: Definition and purpose of simulation in engineering and science, Role of modelling, Classification of simulation types: Physical vs. Numerical, Deterministic vs.

Stochastic, Static vs. Dynamic, Overview of the simulation process: Problem definition, model formulation, Fundamentals of Physical Modeling: Concept of physical models and their applications, Dimensional Analysis: Dimensions and units, homogeneity of equations, Buckingham Pi Theorem and its application, Similitude and Model Laws: Geometric, Kinematic, and Dynamic Similitude, Scaling laws for various physical phenomena (fluid flow, heat transfer, structural mechanics), Distorted models and their implications.

UNIT-2 Experimental Design and Data Analysis in Physical Simulation:

Experimental Design for Physical Models: Planning and execution of physical experiments, Selection of model scales and materials, Measurement Techniques and Instrumentation: Sensors for measuring physical quantities, Data acquisition systems (DAS) and signal conditioning, Calibration of instruments and measurement accuracy, non-intrusive measurement techniques , Data Analysis and Interpretation: Statistical analysis of experimental data, Error analysis and uncertainty quantification, Regression analysis and curve fitting, Visualization of experimental results, Comparison of model results with prototype behavior.

UNIT- 3 Fundamentals of Numerical Simulation: Mathematical Modeling and

Discretization:

Mathematical Modeling of Physical Systems: Conservation laws: Mass, Momentum, Energy, Derivation of governing partial differential equations (PDEs) for: Heat Conduction (Diffusion Equation), Fluid Flow (Navier-Stokes Equations, Continuity Equation), Solid Mechanics (Stress- Strain relations, Equilibrium Equations), Introduction to Numerical Methods: Concept of discretization: Transforming continuous problems into discrete algebraic equations, Finite Difference Method (FDM): Taylor series expansion for approximating derivatives, Forward, Backward, and Central difference schemes, Finite Element Method (FEM): Concept of elements and nodes, Shape functions and interpolation, Weak formulation and weighted residual methods (Galerkin method), Application to 1D bar and heat transfer problems.

UNIT- 4 Advanced Numerical Simulation Techniques and Applications:

Computational Fluid Dynamics (CFD): Navier-Stokes equations and their challenges, Discretization of convective and diffusive terms, Pressure-velocity coupling algorithms (e.g., SIMPLE, PISO), Turbulence modeling (RANS, LES, DNS - conceptual overview), Grid generation and meshing strategies, Applications: Aerodynamics, hydrodynamics, heat exchangers, combustion, Finite Element Analysis (FEA): Review of FEM for 2D problems (plane stress/strain, axisymmetric problems), Discrete Element Method (DEM) for granular materials, Molecular Dynamics (MD) for atomic/molecular level simulations, Boundary Element Method (BEM), Meshless methods, Introduction to Commercial Simulation Software: Overview of popular software packages (e.g., ANSYS, ABAQUS, COMSOL, Open FOAM).

UNIT -5 Validation, Verification, and Advanced Topics:

Verification and Validation (V&V) of Simulations: Verification: Ensuring the numerical model correctly solves the mathematical model, Validation: Ensuring the mathematical model accurately represents the real physical system (comparison with experimental data, analytical solutions), Uncertainty quantification in simulation. Accuracy, Stability, and Convergence: Consistency, stability, and convergence criteria for numerical schemes, Hybrid Simulation: Concept of combining physical and numerical models, Advantages and challenges of hybrid approaches, Examples of coupled simulations (e.g., fluid-structure interaction, thermo-mechanical coupling), Challenges and Future Trends in Simulation: Computational cost and high-performance computing (HPC), Multiphysics and multiscale simulations, Artificial Intelligence and Machine Learning in simulation, Digital Twin concept, Ethical considerations in simulation.

Suggested Readings

• Roache, P. J. (1998). Verification and Validation in Computational Science and Engineering. Hermosa Publishers.
• Oden, J. T., & Carey, G. F. (1999). Finite Elements: Mathematical Aspects. Dover Publications.
• Recent research papers and review articles on simulation and modeling.
• Muralidhar, K., & Sundararajan, T. (2018). Computational Fluid Flow and Heat Transfer. Narosa Publishing House.
• Logan, D. L. (2017). A First Course in the Finite Element Method. Cengage Learning.
• ANSYS/ABAQUS/COMSOL/OpenFOAM User Manuals and Tutorials.
• Versteeg, H. K., & Malalasekera, W. (2007). An Introduction to Computational Fluid Dynamics: The Finite Volume Method. Pearson Education.
• Reddy, J. N. (2019). An Introduction to the Finite Element Method. McGraw-Hill Education.
• Hoffman, J. D., & Frankel, S. (2001). Numerical Methods for Engineers and Scientists. CRC Press.
• Holman, J. P. (2001). Experimental Methods for Engineers. McGraw-Hill Education.
• Figliola, R. S., & Beasley, D. E. (2015). Theory and Design for Mechanical Measurements. John Wiley & Sons.
• Cengel, Y. A., & Cimbala, J. M. (2014). Fluid Mechanics: Fundamentals and Applications. McGraw-Hill Education. (For dimensional analysis and similitude)
• White, F. M. (2016). Fluid Mechanics. McGraw-Hill Education. (For dimensional analysis and similitude). DEPARTMENTAL ELECTIVE – 2