This module provides insights into the stability of second-order hyperbolic equations. It emphasizes the importance of stability in numerical simulations and the implications for practical applications.
This module introduces the fundamental concepts of Computational Fluid Dynamics (CFD) and the principles of conservation laws. It sets the stage for understanding fluid behaviors and equations used in CFD.
This module delves into the Conservation of Mass and Momentum, focusing on the Continuity Equation and the Navier Stokes Equation. These equations form the backbone of fluid dynamics, capturing the essential laws governing flow and momentum transfer.
This module continues the discussion on the Navier Stokes Equation, providing deeper insights into its derivation and implications in fluid dynamics. Understanding this equation is crucial for modeling complex fluid flows.
This module focuses on the Energy Equation and the general structure of conservation equations. Understanding energy conservation is vital for analyzing thermal dynamics in fluid systems and ensuring accurate CFD simulations.
In this module, we classify Partial Differential Equations (PDEs) and examine their physical behaviors. This classification is essential for understanding how different PDEs influence fluid flow and heat transfer.
This module continues the classification of Partial Differential Equations, further exploring different types and their relevance in fluid dynamics. A comprehensive understanding of PDEs is crucial for effective CFD analysis.
This module covers approximate solutions of differential equations, focusing on error minimization principles. Techniques such as variational principles and weighted residual approaches are introduced for effective numerical solutions.
In this module, we delve into variational principles that provide a powerful framework for deriving approximate solutions to differential equations. This method enhances numerical accuracy in CFD applications.
This module introduces the weighted residual approach, a critical method for obtaining approximate solutions. It emphasizes the importance of minimizing errors in numerical computations for fluid flow analysis.
This module discusses the fundamentals of discretization with a focus on the Finite Element Method (FEM). FEM is essential for transforming continuous problems into discrete systems suitable for numerical analysis.
This module expands into other discretization methods, including Finite Difference and Finite Volume Methods. Each method's strengths and weaknesses are examined, providing a comprehensive toolkit for CFD practitioners.
This module continues the discussion on the Finite Volume Method, emphasizing its practical applications in CFD. Understanding this method is key to accurately solving fluid flow and heat transfer problems.
This module presents conceptual basics of the Finite Volume Method, discussing its foundational principles and how they apply to real-world problems in fluid dynamics.
This module covers the implementation of boundary conditions in the Finite Volume Method. Proper boundary condition application is crucial for accurate CFD simulations and results interpretation.
This module discusses the discretization of unsteady state problems using the Finite Volume Method. Techniques for handling time-dependent simulations are explored to ensure stability and accuracy.
This module highlights the important consequences of discretization in unsteady state problems, focusing on numerical stability and convergence to ensure reliable CFD results.
This module discusses the significant consequences of discretizing time-dependent diffusion type problems, addressing common issues and strategies for stability analysis across various methods.
This module focuses on stability analysis of hyperbolic equations, utilizing various schemes such as FTCS, FTFS, FTBS, and CTCS. Understanding stability is crucial for ensuring accurate solutions in CFD.
This module provides insights into the stability of second-order hyperbolic equations. It emphasizes the importance of stability in numerical simulations and the implications for practical applications.
This module serves as a mid-semester assessment review, providing students with a comprehensive overview of key concepts covered thus far. Q&A sessions facilitate deeper understanding and clarification of complex topics.
This module addresses the solution of systems of linear algebraic equations, crucial for numerical analysis in CFD. Various methods for tackling these systems are introduced, enhancing computational efficiency.
This module focuses on elimination methods for solving linear algebraic equations, detailing processes that are pivotal in simplifying complex systems for efficient numerical solutions.
This module continues the discussion on elimination methods, addressing error analysis and optimization strategies that improve the accuracy of solutions in linear algebraic equations.
This module examines error analysis in elimination methods, offering insights into potential pitfalls and strategies to enhance accuracy in numerical computations for CFD applications.
This module discusses iterative methods for solving systems of linear algebraic equations, outlining their advantages and applications in CFD scenarios. These methods offer efficient alternatives to direct solving techniques.
This module continues the exploration of iterative methods, providing examples and practical applications. Students learn how to implement these methods effectively in computational fluid dynamics.
This module presents further examples of iterative methods, emphasizing their implementation in diverse CFD scenarios. Students gain hands-on experience in applying these techniques to real-world problems.
This module discusses combinations of iteration and elimination techniques, showcasing how integrating methods can enhance solution accuracy and efficiency in numerical fluid dynamics.
This module focuses on Gradient Search Methods, detailing their applications and advantages in optimizing solutions within CFD contexts. Understanding these methods is vital for efficient simulations.
This module continues the discussion on Gradient Search Methods, providing additional insights and practical examples that illustrate their effectiveness in solving complex CFD problems.
This module covers the discretization of convection-diffusion equations using a Finite Volume approach. Emphasis is placed on understanding the underlying principles that govern these processes.
This module continues the exploration of the Finite Volume approach for convection-diffusion equations, detailing advanced techniques and practical applications relevant to real-world fluid dynamics scenarios.
This module delves further into the Finite Volume approach for convection-diffusion equations, ensuring students understand the complexities and intricacies involved in applying these techniques.
This module provides a comprehensive overview of the Finite Volume approach for convection-diffusion equations. It emphasizes the importance of understanding the method's foundations and applications in practical scenarios.
This module explores the discretization of Navier Stokes equations, focusing on methods such as the stream function-vorticity approach and primitive variable approach, which are crucial for solving fluid flow problems.
This module continues the discussion on the discretization of Navier Stokes equations, providing deeper insights into the methods and their applications in CFD simulations.
This module further examines the discretization methods for Navier Stokes equations, focusing on practical applications and considerations necessary for effective CFD modeling.
This module covers unstructured grid formulation, discussing its significance in CFD. Understanding unstructured grids allows for greater flexibility and accuracy in representing complex geometries.
This module discusses the practical aspects of implementing a CFD code, focusing on the essential steps and considerations involved in successful code development and application.
This module introduces turbulence modeling, focusing on foundational concepts and techniques used to simulate turbulent flows accurately. Understanding turbulence is essential for realistic fluid dynamics modeling.
This module continues the exploration of turbulence modeling, providing additional insights and methodologies for accurately capturing the complexities of turbulent flows in simulations.
This module serves as a review of end-semester questions, facilitating discussion and clarification of key concepts covered throughout the course. It helps reinforce learning and prepare for assessments.