This module presents the stability problem statement in numerical methods. Students will explore the conditions under which numerical solutions remain stable, which is crucial for ensuring reliable results in CFD.
This module serves as an introduction to Computational Fluid Dynamics, exploring the motivation behind CFD. It outlines the essential CFD approaches, the significance of computational techniques in understanding fluid behavior, and sets the stage for advanced learning.
This module illustrates the CFD approach using a worked example, showcasing how computational methods can be applied to solve real fluid flow problems. The example guides students through the process of formulating and solving a CFD problem, enhancing understanding through practical application.
In this module, the Eulerian approach to fluid dynamics is introduced, focusing on conservation equations. Students will derive the mass conservation equation, which is fundamental in fluid mechanics, enabling them to understand how mass is conserved in a control volume.
This module continues the discussion of the Eulerian approach, further exploring conservation equations. It delves into the derivation of the mass conservation equation, reinforcing the foundational concepts necessary for understanding fluid flow and the principles governing it.
This module addresses forces acting on a control volume and the stress tensor. Understanding these concepts is crucial for analyzing fluid behavior and the interactions between fluid elements. Students will learn how to apply these principles in practical CFD scenarios.
This module focuses on the kinematics of deformation in fluid flow, detailing the relationship between stress and strain rate. Students will gain insights into how fluids deform under various forces, which is essential for understanding fluid mechanics.
This module discusses the equations governing the flow of incompressible fluids. These equations are critical for CFD simulations, allowing students to predict fluid behavior accurately under various conditions.
This module introduces spatial discretization methods for simple flow domains, providing students with the foundational techniques necessary for breaking down complex fluid problems into manageable numerical solutions.
In this module, students will learn about finite difference approximations of different orders of accuracy for derivatives. This knowledge is fundamental for developing accurate numerical methods in CFD and improving solution precision.
This module covers one-sided high-order accurate approximations as well as explicit and implicit formulations. Understanding these concepts is vital for refining numerical methods and achieving better computational results in fluid dynamics.
This module focuses on the numerical solution of the unsteady advection equation using various finite methods. Students will learn how to apply these techniques to solve transient fluid flow problems effectively.
In this module, students will analyze the need for scrutinizing discretization schemes for numerical simulations. The concepts of consistency will be introduced, providing a strong foundation for understanding numerical stability and accuracy.
This module presents the stability problem statement in numerical methods. Students will explore the conditions under which numerical solutions remain stable, which is crucial for ensuring reliable results in CFD.
In this module, students will conduct a consistency and stability analysis of the unsteady diffusion equation. This analysis is essential for understanding the behavior of numerical solutions and ensuring their accuracy.
This module focuses on interpreting stability conditions and conducting stability analysis of generic scalar equations. Students will learn to evaluate the stability of numerical methods applied to fluid dynamics problems.
This module introduces a template for the generic scalar transport equation and discusses its extension to solutions. This foundational understanding is pivotal for tackling more complex fluid flow problems.
In this module, students will illustrate the application of the template using the MacCormack scheme. This practical approach helps solidify understanding of numerical methods in CFD.
This module discusses the stability limits of the MacCormack scheme, focusing on the conditions required for stable numerical solutions. Understanding these limits is essential for effective CFD modeling.
This module introduces the artificial compressibility method and the streamfunction-vorticity method, essential tools for solving fluid dynamics equations, especially in incompressible flow scenarios.
In this module, the pressure equation method for solving Navier-Stokes equations is introduced. Students will learn to apply this method to analyze fluid flow under various conditions.
This module presents the pressure-correction approach to solving Navier-Stokes equations on staggered grids. This method enhances the accuracy and stability of numerical simulations in fluid flow.
This module emphasizes the need for efficient solutions of linear algebraic equations in CFD simulations. Understanding these methods is vital for optimizing computational resources and improving simulation speed.
This module introduces direct methods for solving linear algebraic equations, focusing on the Gaussian elimination method. Students will learn the theoretical foundations and practical applications of these techniques in CFD.
This module discusses the Gauss-Jordan method, LU decomposition method, TDMA, and the Thomas algorithm. These techniques are essential for solving complex systems of equations in CFD efficiently.
This module covers basic iterative methods for linear algebraic equations, introducing the point-Jacobi method. Students will understand the iterative approach's importance in enhancing computational efficiency in CFD.
This module analyzes the convergence of basic iterative schemes, emphasizing the diagonal dominance condition. Understanding convergence is crucial for ensuring that iterative methods yield reliable solutions in CFD.
This module applies iterative methods to solve the Laplace equation, illustrating their practical use in CFD. Students will see how these methods can effectively tackle real-world fluid problems.
This module delves into advanced iterative methods, including the Alternating Direction Implicit Method and Operator Splitting. These techniques are vital for enhancing solution accuracy and computational efficiency in CFD simulations.
This module introduces advanced iterative methods such as the Strongly Implicit Procedure and the Conjugate Gradient method. These methods are essential for efficiently solving large systems of equations in CFD.
This module provides an illustration of the Multigrid method for solving the Laplace equation. Students will learn how this method accelerates convergence and improves computational efficiency in CFD.
This module offers an overview of numerical solutions for Navier-Stokes equations in simple domains. Understanding these methods lays the groundwork for analyzing complex fluid flow situations.
In this module, students derive the energy conservation equation, which is fundamental for analyzing thermal effects in fluid flow. This equation plays a critical role in many practical applications.
This module focuses on the derivation of the species conservation equation, including considerations for chemical reactions. This understanding is vital for modeling reactive flows in CFD.
This module discusses turbulence, its characteristics, and how to manage fluctuations in fluid flows. Understanding turbulence is crucial for accurate CFD simulations of real-world scenarios.
In this module, students will derive the Reynolds-averaged Navier-Stokes equations, which are pivotal for analyzing turbulent flows. This foundational knowledge is essential for advanced CFD modeling.
This module discusses Reynolds stresses in turbulent flow, focusing on time and length scales of turbulence. Understanding these concepts is vital for accurate turbulence modeling in CFD.
This module introduces a one-equation model for turbulent flow, providing a simplified approach to turbulence modeling. This model is significant for practitioners aiming to apply CFD in various engineering applications.
This module covers a two-equation model for turbulent flow, detailing its numerical calculation. This model offers an advanced approach to turbulence modeling, essential for comprehensive CFD analysis.
This module discusses methods for calculating the near-wall region in turbulent flow, including the wall function approach. These techniques are crucial for accurately modeling boundary layers in CFD simulations.
This module highlights the need for special methods to deal with irregular flow geometry in CFD. Understanding these methods is essential for accurate modeling in complex engineering applications.
In this module, students will learn about the transformation of governing equations, illustrated through the Laplace equation. This transformation approach is essential for solving complex fluid problems.
This module covers the finite volume method for complicated flow domains, focusing on its application in CFD. This method is crucial for analyzing fluid behavior in complex geometries.
This module discusses the finite volume method for the general case, emphasizing its versatility in various fluid dynamics applications. Students will learn how to apply this method effectively in CFD.
This module focuses on generating structured grids for irregular flow domains using algebraic methods. Students will learn the importance of grid generation techniques in enhancing CFD simulation accuracy.
This module addresses unstructured grid generation and domain nodalization, which are essential for accurately modeling complex fluid flow scenarios in CFD. Understanding these techniques is crucial for computational efficiency.
This module introduces the Delaunay triangulation method for unstructured grid generation. This method is widely used in CFD for creating high-quality grids that improve simulation results.
This module presents the co-located grid approach for irregular geometries, focusing on pressure correction equations. This approach enhances the accuracy of numerical solutions in CFD for complex flows.