MIT Numerical Methods for PDE Lecture 8: Continuous solution and characteristics lines

preview_player
Показать описание

  1. Aerodynamic CFD
Рекомендации по теме
MIT Numerical Methods 0:14:54

MIT Numerical Methods for PDE Lecture 1: Finite difference solution of heat equation

MIT Numerical Methods 0:12:27

MIT Numerical Methods for Partial Differential Equations Lecture 1: Heat Equation

MIT Numerical Methods 0:14:35

MIT Numerical Methods for PDE Lecture 11: System of Conservation Laws

But what is 0:17:39

But what is a partial differential equation? | DE2

MIT Numerical Methods 0:12:02

MIT Numerical Methods for PDE Lecture 9: Non-uniqueness of solution to conservation laws

MIT Numerical Methods 0:11:08

MIT Numerical Methods for PDE Lecture 13: Introduction to Finite Element

MIT Numerical Methods 0:13:32

MIT Numerical Methods for PDE Lecture 13: Projection and finite element for the Poisson's equat...

MIT Numerical Methods 0:09:57

MIT Numerical Methods for PDE Lecture 3: Domain mapping Q&A

MIT Numerical Methods 0:10:19

MIT Numerical Methods for PDE Lecture 2: Review and FD for Poisson's equation

MIT Numerical Methods 0:14:59

MIT Numerical Methods for PDE Lecture 21: Introduction to high fidelity design and supercomputing

MIT Numerical Methods 0:12:57

MIT Numerical Methods for PDEs Lecture 18: PDE-based simulations in science and engineering

MIT Numerical Methods 0:10:40

MIT Numerical Methods for PDE Lecture 10: Godunov Scheme Demo

MIT Numerical Methods 0:14:50

MIT Numerical Methods for PDE Lecture 2: Stability analysis for Poisson's equation

MIT Numerical Methods 0:08:49

MIT Numerical Methods for PDE Lecture 13: Projection and finite element Q&A

MIT Numerical Methods 0:10:35

MIT Numerical Methods for PDE Lecture 13: Flux limiter review and demo

MIT Numerical Methods 0:13:21

MIT Numerical Methods for PDE Lecture 3: Finite Difference for 2D Poisson's equation

MIT Numerical Methods 0:13:27

MIT Numerical Methods for PDEs Lecture 15: Math Foundation of Finite Element: function spaces

22. Partial Differential 0:49:34

22. Partial Differential Equations 1

MIT Numerical Methods 0:06:28

MIT Numerical Methods for PDE Lecture 8: Clarifications on Project 2

MIT Numerical Methods 0:14:58

MIT Numerical Methods for PDE Lecture 6: Diagnosis of how multigrid works

MIT Numerical Methods 0:11:38

MIT Numerical Methods for PDE Lecture 2: Constructing Finite Difference Approximation

MIT Numerical Methods 0:10:06

MIT Numerical Methods for PDE Lecture 8: Continuous solution and characteristics lines

MIT Numerical Methods 0:05:04

MIT Numerical Methods for PDE Lecture 13: More on Projection

MIT Numerical Methods 0:13:06

MIT Numerical Methods for Partial Differential Equations Lecture 1: Convection Diffusion Equation

Комментарии
Автор

Hello Mr. Wang,

Can we rather say that if :

du/dt were to be zero (implying no change in slope of the solution with respect to time)

when : the governing equations hold true for the smooth region of the solution

then : dx/dt will have to be equal to (del.f/del.u)


I am able to make sense of the things in this order
rather than

when we already define the characteristic line as a straight line by saying X = ct, and then saying that it will be a straight line if c= del.f/del.u which will give du/dt = 0, because the governing equations were true and thus the slope doesn't change along the characteristic line.


Kind Regards
Suyash Sharma

suyashsharma
Автор

Hello,

Tell me if i am wrong, the solution f '(u) = sin(u), then burgers equation would be f(u) = -cos x, which it isn't, so did you just take solution of burger's eqn here as sin u for demonstrating purposes only?

suyashsharma