Course Details

Mathematical Description of Transport Phenomena: Conservation laws. Fundamental differential equations. Phenomenological laws. Laws governing the sources. General form of conservation equations. Generalized Conservation Law.

Computational Methods ? Discretization: Classification of differential equations. Nature of the well-defined problem. Numerical solution of transport equation. Derivative approximation by finite differences. Derivative approximation by polynomial interpolation. Derivative approximation using Taylor series. Accuracy of derivative approximation. Expressions of finite differences. Expressions of first and second derivative.

Basic Properties of Numerical Schemes: Pure convection equation. Discretization of partial derivatives equations. Discretization of convection equation (FTBS scheme). Accurate order of discretization scheme. Consistency, Stability, Convergence of numerical scheme. Stability analysis ? Von Neumann Method. Response function for convection equation. Latitude and phase of the response function. Stability of FTBS scheme.

Pure Diffusion Equation: One-dimensional problems ? Model equation. Explicit schemes. FTCS scheme: Truncation error analysis. Stability analysis. LeapFrog scheme. DuFort-Frankel scheme. Implicit numerical schemes: General form. Truncation error analysis. Stability analysis.

Convection ? Diffusion Equation: Analytical solution. FTCS scheme: Difference equations. Consistency, Stability, Numerical diffusion of scheme. Upwind-Differencing Scheme: Difference equations. Consistency, Stability, Numerical diffusion of scheme.

Finite Volume Method: Integration of Transport Equation. Integral form. Computational grid – Control volumes. Discretization of the transport equation. Treatment of convection and diffusion terms. Central-Differencing scheme. Upwind-Differencing scheme. False Diffusion. Hybrid scheme. Treatment of the source term. Final form of the descritized transport equation. Solution of the hydrodynamic field: SIMPLE and SIMPLEC algorithms. Boundary conditions for scalar. Boundary conditions for momentum equation ? Wall functions. Fixed-field-value boundary condition. Final form of the source term.

Solution of Systems of Linear Algebraic Equations: Problem formulation. Direct methods: Method of Gauss Elimination. LU-decomposition method. Thomas Algorithm. Evaluation of direct methods. Iterative Methods: General structure of iterative methods. Point-by-Point solution method. Jacobi method. Gauss-Seidel method. Sequential Relaxation method. Line-by-Line method: solution and acceleration of the method. SIP method.

Computer Simulation of Transport Phenomena: Problem formulation: Physico-chemical mechanisms. Boundary conditions. Spatial distribution of solution domain. Fluid properties. Simulation procedure: Discretization of equations. Solution of algebraic systems. Solution results.

Computational Fluid Dynamics Code: Code description. Structure of input file. Techniques of grid generation. Definition of fluid properties. Introduction of boundary conditions. Introduction of terms of differential equations. Iterative solution methods. Convergence: Procedure, Criteria, Settings. Study of grid-independent solution. Display and treatment of results. Applications: Solution of turbulent flow problems and laminar flow problems with chemical reaction using the PHOENICS software.