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Introduction to Finite Volume Methods I

Introduction to Finite Volume Methods I. Instructor: Prof. Ashoke De, Department of Aerospace Engineering, IIT Kanpur. The Finite Volume Method (FVM) is one of the widely used numerical techniques in the scientific community and in industry as well. In this approach, the partial differential equations that represent the conservation laws to simulate uid flow, heat transfer, and other related physical phenomena, are transformed over differential volumes into discrete algebraic equations over nite volumes (or elements or cells). Thereafter, the system of algebraic equations is solved to compute the values of the dependent variable for each of the elements to represent the physical processes. (from nptel.ac.in)

Lecture 33 - Gradient Calculation for Diffusion Equation I


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Fundamentals of Finite Volume Methods
Lecture 01 - Introduction
Lecture 02 - Governing Equations and Discretization
Lecture 03 - Boundary Conditions and Classification of PDEs
Lecture 04 - Mathematical Description of Fluid Flow
Lecture 05 - Mathematical Description of Fluid Flow (cont.)
Discretization Process and Taylor Series
Lecture 06 - Discretization Process I
Lecture 07 - Discretization Process II
Lecture 08 - Discretization Process III
Lecture 09 - Taylor Series
Lecture 10 - Taylor Series (cont.)
Derivatives and Errors
Lecture 11 - Derivatives and Errors
Lecture 12 - Derivatives and Errors (cont.)
Lecture 13 - Grid Transformation
Lecture 14 - Finite Volume Formulation
Lecture 15 - Finite Volume Formulation (cont.)
Finite Volume Formulation
Lecture 16 - Properties of Discretized Equations
Lecture 17 - Introduction to Finite Volume Mesh
Lecture 18 - Structured Mesh System
Lecture 19 - Unstructured Mesh System
Lecture 20 - Unstructured Mesh System (cont.)
Finite Volume Mesh Properties
Lecture 21 - Properties of Unstructured Mesh
Lecture 22 - Properties of Unstructured Mesh (cont.)
Lecture 23 - Finite Volume Discretization of Diffusion Equation I
Lecture 24 - Finite Volume Discretization of Diffusion Equation II
Lecture 25 - Finite Volume Discretization of Diffusion Equation III
Discretization of Diffusion Equation
Lecture 26 - Discretization of Diffusion Equation for Cartesian Orthogonal Systems
Lecture 27 - Discretization of Diffusion Equation for Cartesian Orthogonal Systems (cont.)
Lecture 28 - Calculation of Diffusivity
Lecture 29 - Discretization of Diffusion Equation for Non-Cartesian Orthogonal Systems
Lecture 30 - Discretization of Diffusion Equation for Non-Orthogonal Systems I
Discretization of Diffusion Equation and Gradient Calculation
Lecture 31 - Discretization of Diffusion Equation for Non-Orthogonal Systems II
Lecture 32 - Discretization of Diffusion Equation for Non-Orthogonal Systems III
Lecture 33 - Gradient Calculation for Diffusion Equation I
Lecture 34 - Gradient Calculation for Diffusion Equation II
Lecture 35 - Gradient Calculation for Diffusion Equation III
Solution of Linear System of Equations
Lecture 36 - Properties of Matrices
Lecture 37 - Properties of Matrices (cont.)
Lecture 38 - Error Analysis I
Lecture 39 - Error Analysis II
Lecture 40 - Error Analysis III