Search for tag: "differential equations"

35 Media

Eduard Feireisl - Friday 12 November duration 36 minutes 13 seconds Eduard Feireisl - Friday 12 November Eduard Feireisl - Friday 12 November	Eduard Feireisl - Friday 12 November 08 Nov- 12 Nov 2021ICMS hosted the Convex Integration and Nonlinear Partial Differential Equations workshopOn strong continuity of weak solutions to the compressible Euler equations Eduard Feireisl… convex integration nonlinear differential equations function solutions energy solution functions density points problem continuity statement equation convex point condition integration profile boxes form kind degradation From Simon Kershaw 0 likes 35 plays 0 Licence Type All rights reserved
Partial Differential Equations Lecture 10 -… duration 7 minutes 17 seconds Partial Differential Equations Lecture 10 -… Partial Differential Equations Lecture 10 - Results	Partial Differential Equations Lecture 10 - Results In the last part of this lecture we look at the results we obtain to the test problem and look forward to solving real fluid dynamics problems using commercial solvers in CFD5. shallow water equations numerical methods partial differential equations metre water conditions equations velocity metres depression solution left side condition problems height steps problem dynamics flow direction thing shock From David Ingram 0 likes 119 plays 0 Course Code SCEE09004 Publisher School of Engineering Licence Type Creative Commons - Attribution Language English Date Created February 22nd, 2021
Partial Differential Equations Lecture 10 - The… duration 6 minutes 46 seconds Partial Differential Equations Lecture 10 - The… Partial Differential Equations Lecture 10 - The Solver	Partial Differential Equations Lecture 10 - The Solver We now introduce a family of test problems and look at the Matlab code needed to solver the shallow water equations. shallow water equations numerical methods partial differential equations solution hand equations conditions characteristics water problem fluxes velocity programme height characteristic problems flow boundary areas quantities depression side point From David Ingram 0 likes 109 plays 0 Course Code scee09004 Publisher School of Engineering Licence Type Creative Commons - Attribution Language English Date Created February 22nd, 2021
Partial Differential Equations Lecture 10 -… duration 10 minutes 50 seconds Partial Differential Equations Lecture 10 -… Partial Differential Equations Lecture 10 - Shallow Water Equations	Partial Differential Equations Lecture 10 - Shallow Water Equations In this lecture we extend our solver to apply to a system of equations in one spatial dimension. In this case we are solving the St Vennant, or Shallow Water Equations. shallow water equations partial differential equations numerical methods equations matrix conservation momentum phi mass advection water root lambda linear inverse q2 eigenvalues times speed equation form channel term From David Ingram 0 likes 168 plays 0 Course Code SCEE09004 Publisher School of Engineering Licence Type Creative Commons - Attribution Language English Date Created February 22nd, 2021
Partial Differential Equations Lecture 9 - Results duration 10 minutes 13 seconds Partial Differential Equations Lecture 9 - Results Partial Differential Equations Lecture 9 - Results	Partial Differential Equations Lecture 9 - Results Here we look in detail at the results from the test problem and discuss dispersive and dissipative errors. numerical methods hyperbolic equation fractional steps partial differential equations solution amplitude test grid dispersion 3d dissipation error kind problems conditions shape concentration equations delta errors bit wave lots loss From David Ingram 0 likes 118 plays 0 Course Code SCEE09004 Publisher School of Engineering Licence Type Creative Commons - Attribution Language English Date Created February 16th, 2021
Partial Differential Equations Lecture 9 -… duration 7 minutes 25 seconds Partial Differential Equations Lecture 9 -… Partial Differential Equations Lecture 9 - MacCormack method in 2D	Partial Differential Equations Lecture 9 - MacCormack method in 2D This part of the lecture develops a 2D solver using the method of Fractional Steps and the MacCormack scheme and applies it to a test problem hyperbolic equation fractional steps numerical methods partial differential equations operator problem conditions function test step direction bit 2pi values delta 3e solution times scheme lecture rise corrector predictor timestep From David Ingram 0 likes 320 plays 0 Course Code SCEE09004 Publisher School of Engineering Licence Type Creative Commons - Attribution Language English Date Created February 16th, 2021
Partial Differential Equations Lecture 9 - Two… duration 9 minutes 39 seconds Partial Differential Equations Lecture 9 - Two… Partial Differential Equations Lecture 9 - Two and three dimensional solvers	Partial Differential Equations Lecture 9 - Two and three dimensional solvers In this lecture we look at operator splitting and the method of fractional steps which can be used to solve 2 and 3D problems with 1D schemes. fractional steps hyperbolic equation partial differential equations solution series sequence operator problems times step operators term taylor equation equations problem lecture steps schemes point diffusion middle derivative From David Ingram 0 likes 215 plays 0 Course Code SCEE09004 Publisher School of Engineering Licence Type Creative Commons - Attribution Language English Date Created February 16th, 2021
Partial Differential Equations, Lecture 8c: MUSCL… duration 5 minutes 22 seconds Partial Differential Equations, Lecture 8c: MUSCL… Partial Differential Equations, Lecture 8c: MUSCL Schemes	Partial Differential Equations, Lecture 8c: MUSCL Schemes We look briefly at how MUSCL schemes use weighted interpolation of fluxes as an alternative to the TVD schemes. muscl scheme hyperbolic equation partial differential equations schemes flux muscle scheme half fluxes tvd methods method problem points interpolation cell function conservation lecture discontinuities curves parabolic piecewise From David Ingram 0 likes 622 plays 0 Course Code SCEE09004 Publisher School of Engineering Licence Type Creative Commons - Attribution Language English Date Created February 15th, 2021
Partial Differential Equations, Lecture 8b: TVD… duration 5 minutes 26 seconds Partial Differential Equations, Lecture 8b: TVD… Partial Differential Equations, Lecture 8b: TVD MacCormack	Partial Differential Equations, Lecture 8b: TVD MacCormack Here we implement the MacCormack scheme with a TVD correction in Matlab and apply it to a test problem tvd scheme maccormack method hyperbolic equation partial differential equations scheme solution correction function grid step tvd bit minus formula cell conditions prediction equations predictor steps discontinuities selection seconds likes From David Ingram 0 likes 402 plays 0 Course Code SCEE09004 Publisher School of Engineering Licence Type Creative Commons - Attribution Date Created February 15th, 2021
Partial Differential Equations, Lecture 8a:… duration 8 minutes 24 seconds Partial Differential Equations, Lecture 8a:… Partial Differential Equations, Lecture 8a: Monotone Methods for Conservation Laws	Partial Differential Equations, Lecture 8a: Monotone Methods for Conservation Laws In this lecture we look at schemes which are not prone to producing the spurious "Gibbs" oscillations we saw in the last lecture. We start b talking about TVD schemes tvd scheme hyperbolic equation partial differential equations scheme function gradient solution functions variation oscillations equations property correction schemes limiter mode 50k curve phi minus inequalities half idea From David Ingram 0 likes 226 plays 0 Course Code SCEE09004 Publisher School of Engineering Licence Type Creative Commons - Attribution Language English Date Created February 15th, 2021
Partial Differential Equations, Lecture 7a:… duration 4 minutes 5 seconds Partial Differential Equations, Lecture 7a:… Partial Differential Equations, Lecture 7a: Numerical solution of hyperbolic PDEs.	Partial Differential Equations, Lecture 7a: Numerical solution of hyperbolic PDEs. A lecture introducing numerical methods for hyperbolic PDEs hyperbolic equation partial differential equations numerical methods equation schemes scheme equations space operator series taylor term linear difference delta derivative advection lecture form eviction expansion kind x. From David Ingram 0 likes 266 plays 0 Course Code SCEE09004 Publisher School of Engineering Licence Type Creative Commons - Attribution Language English Date Created February 8th, 2021
Elliptic PDE Analytical methods Part 3: Boundary… duration 19 minutes 52 seconds Elliptic PDE Analytical methods Part 3: Boundary… Elliptic PDE Analytical methods Part 3: Boundary conditions	Elliptic PDE Analytical methods Part 3: Boundary conditions Video introducing different boundary conditions as well as the concept of well-posed problems. pde3 engineering mathematics elliptic partial differential equations lecture conditions boundary solution condition equation domain equations heat side flow temperature boundaries solutions problem hand change laplace types points question From Daniel Friedrich 0 likes 532 plays 0 Course Code SCEE09004 Publisher Daniel Friedrich Licence Type Creative Commons - Attribution Language English Date Created January 10th, 2021
Introduction PDE Analytical methods Part 2:… duration 19 minutes 14 seconds Introduction PDE Analytical methods Part 2:… Introduction PDE Analytical methods Part 2: Applications	Introduction PDE Analytical methods Part 2: Applications Video with some example applications of partial differential equations in mechanical engineering. pde3 engineering mathematics lecture introduction partial differential equations From Daniel Friedrich 0 likes 369 plays 0 Course Code SCEE09004 Publisher Daniel Friedrich Licence Type Creative Commons - Attribution Language English Date Created December 14th, 2020
Introduction PDE Analytical methods Part 1: PDE… duration 25 minutes 49 seconds Introduction PDE Analytical methods Part 1: PDE… Introduction PDE Analytical methods Part 1: PDE vs ODE	Introduction PDE Analytical methods Part 1: PDE vs ODE Introduction to PDEs and comparison to ODEs pde3 lecture engineering mathematics introduction partial differential equations From Daniel Friedrich 0 likes 516 plays 0 Course Code SCEE09004 Publisher Daniel Friedrich Licence Type Creative Commons - Attribution Language English Date Created December 14th, 2020
Lecture 6 Part 3: Driven, damped oscillators duration 7 minutes 24 seconds Lecture 6 Part 3: Driven, damped oscillators Lecture 6 Part 3: Driven, damped oscillators	Lecture 6 Part 3: Driven, damped oscillators Here we add a driving force to the oscillator and consider how the standard form of the equation is modified. We look at the amplification factor and see what happens under resonant conditions. differential equations frequency omega force bridge form resonance function amplitude response end side vortex lecture equations construction tacoma graph choices cases oscillation From David Ingram 0 likes 556 plays 0 Course Code scee08009 Licence Type Creative Commons - Attribution Language English Date Created July 10th, 2020
Lecture 6 Part 2: Damped oscillators duration 6 minutes 30 seconds Lecture 6 Part 2: Damped oscillators Lecture 6 Part 2: Damped oscillators	Lecture 6 Part 2: Damped oscillators We extend the ideas from the first part of the lecture to oscillators which include damping effects. Writing the governing equation in a standard form and looking at the meaning of the damping… differential equations omega equation times term energy roots resistance air pendulum cantilever envelope behavior form side force theta amplitude point displacement decay From David Ingram 0 likes 586 plays 0 Course Code scee08009 Licence Type Creative Commons - Attribution Language English Date Created July 10th, 2020