[CFD | ENG] Finite Volume Methods for Linear Hyperbolic Conservation Laws скачать в хорошем качестве

[CFD | ENG] Finite Volume Methods for Linear Hyperbolic Conservation Laws

This video continues the previous video called "Introduction to linear hyperbolic conservation laws". Here, we will give a brief introduction to the finite volume method (FVM), which is the most popular numerical method used to solve these kinds of PDE's. By integrating the linear advection equation, we will derive the standard FVM equation, which depends on the value at the old-time step and on the fluxes at the cell borders. We will discuss some of the most common and simplest schemes that estimate these fluxes in order to obtain the value of the solution at the new-time step: the central, Lax-Friedrichs, Lax-Wendroff and Upwind schemes. Lastly, we will briefly talk about the Courant-Friedrichs-Lewy (CFL) condition and will show the local truncation errors of each scheme to determine the order of consistency of the FVM. This video is part of a two lectures series about "Linear Hyperbolic Conservation Laws". The first lecture can be found here:    • [CFD | ENG] Introduction to linear hyperbo...   Timestamps 00:22 Overview of the presentation 01:02 Introduction to the finite volume method 08:30 The general equation of the FVM 13:11 The Central scheme 15:25 The Lax-Friedrichs scheme 17:06 The Lax-Wendroff scheme 19:19 The basic idea behind the upwind method 25:31 The upwind method 28:12 Alternative form for the equations of the upwind method 33:31 The Courant-Friedrichs-Lewy (CFL) condition 37:17 Definition of local truncation error 41:04 Consistency of the upwind method 44:21 Consistency of the Lax-Friedrichs and Lax-Wendroff schemes 47:26 Final comments and references Related videos: "Introduction to the finite volume method in CFD":    • [CFD | ENG] Introduction to the finite vol...   Links of interest Personal webpage where you can read more about my research related to fluid dynamics and other popular-science articles: https://hugocastillocom.wordpress.com