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September 23, 2023

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Description

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)

Course Curriculum

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

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