Physical And Numerical Simulation

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.

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.

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.

• 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).

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.