
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…
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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.
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SCEE09004 Publisher
School of Engineering Licence Type
Creative Commons  Attribution Language
English Date Created
February 22nd, 2021


We now introduce a family of test problems and look at the Matlab code needed to solver the shallow water equations.
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scee09004 Publisher
School of Engineering Licence Type
Creative Commons  Attribution Language
English Date Created
February 22nd, 2021


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.
Course Code
SCEE09004 Publisher
School of Engineering Licence Type
Creative Commons  Attribution Language
English Date Created
February 22nd, 2021


Here we look in detail at the results from the test problem and discuss dispersive and dissipative errors.
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SCEE09004 Publisher
School of Engineering Licence Type
Creative Commons  Attribution Language
English Date Created
February 16th, 2021


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
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SCEE09004 Publisher
School of Engineering Licence Type
Creative Commons  Attribution Language
English Date Created
February 16th, 2021


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.
Course Code
SCEE09004 Publisher
School of Engineering Licence Type
Creative Commons  Attribution Language
English Date Created
February 16th, 2021


We look briefly at how MUSCL schemes use weighted interpolation of fluxes as an alternative to the TVD schemes.
Course Code
SCEE09004 Publisher
School of Engineering Licence Type
Creative Commons  Attribution Language
English Date Created
February 15th, 2021


Here we implement the MacCormack scheme with a TVD correction in Matlab and apply it to a test problem
Course Code
SCEE09004 Publisher
School of Engineering Licence Type
Creative Commons  Attribution Date Created
February 15th, 2021


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
Course Code
SCEE09004 Publisher
School of Engineering Licence Type
Creative Commons  Attribution Language
English Date Created
February 15th, 2021


A lecture introducing numerical methods for hyperbolic PDEs
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SCEE09004 Publisher
School of Engineering Licence Type
Creative Commons  Attribution Language
English Date Created
February 8th, 2021


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.
Course Code
scee08009 Licence Type
Creative Commons  Attribution Language
English Date Created
July 10th, 2020


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…
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scee08009 Licence Type
Creative Commons  Attribution Language
English Date Created
July 10th, 2020


Here we look at how the the same (or a very similar) differential equation applies to several different engineering problems. We consider cantilevers, pendulums and a floating buoy.
Course Code
SCEE08009 Licence Type
Creative Commons  Attribution Language
English Date Created
July 10th, 2020


Here we look at some more general oscillators and their phase portraits and consider how plotting vector plots can be useful for understanding autonomous systems.
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SCEE08009 Licence Type
Creative Commons  Attribution Language
English Date Created
July 7th, 2020


How do understand the behaviour of the oscillator, why is plotting velocity against displacement useful? What are stationary points and limit cycles?
Course Code
SCEE08009 Licence Type
Creative Commons  Attribution Language
English Date Created
July 7th, 2020
