Videos tagged cfd
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ME 702 - Computational Fluid Dynamics - Video Lesson 22
NEW ! (August 2014) Prof. Barba is teaching a MOOC titled "Practical Numerical Methods with Python." Check it out:
http://openedx.seas.gwu.edu/courses/GW/MAE6286/2014_fall/about
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Euler equations, in [...]conservation form: continuity equation, momentum equation, energy equation. “Short form†of the full Euler equations using vector notation, and the analogy with the 1D convection equation that allows us to use the same schemes that we have been studying thus far.
This video is part of the open courseware prepared by Prof. Lorena A. Barba.
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ME 702 - Computational Fluid Dynamics - Video Lesson 21
NEW ! (August 2014) Prof. Barba is teaching a MOOC titled "Practical Numerical Methods with Python." Check it out:
http://openedx.seas.gwu.edu/courses/GW/MAE6286/2014_fall/about
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Burgers’ equation [...]debrief—What happens with MacCormack method? Watch out for the possibility of over-shoots destroying stability! As you decrease CFL number, there are more dispersive oscillations. Among these schemes, which is best? Lax-Friedrichs, Lax-Wendroff, MacCormack? When solving Burgers’ equation with the implicit Beam & Warming method, you use the Thomas algorithm to solve a tri-diagonal system. If you use a source like Wikipedia for the Thomas algorithm, watch out! We have boundary conditions ...
This video is part of the open courseware prepared by Prof. Lorena A. Barba.
For more, visit: http://lorenabarba.com
Follow: https://twitter.com/LorenaABarba
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ME 702 - Computational Fluid Dynamics - Video Lesson 20
NEW ! (August 2014) Prof. Barba is teaching a MOOC titled "Practical Numerical Methods with Python." Check it out:
http://openedx.seas.gwu.edu/courses/GW/MAE6286/2014_fall/about
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Burgers’ equation [...]debrief—Review of the discretization in conservative form. For hyperbolic equations, we have ‘strong solutions’ and ‘weak solutions’; the conservarive form lets us obtain weak solutions (e.g., shocks). What happens with the Lax-Friedrichs scheme? It is a first-order scheme and exhibits numerical diffusion; stability requires CFL less than 1 (defining CFL number with the maximum value of velocity)f. With different CFL numbers, we see more numerical diffusion as the CFL number is decreased and the quality of the solution deteriorates. Note that there is cancellation of errors with CFL=2 and the solution is exact! (similarly to the linear convection example with CFL=1.) With the Lax-Wendroff scheme, which is second order, we see dispersion errors; with different CFL numbers, we see more oscillations as CFL decreases.
This video is part of the open courseware prepared by Prof. Lorena A. Barba.
For more, visit: http://lorenabarba.com
Follow: https://twitter.com/LorenaABarba
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ME 702 - Computational Fluid Dynamics - Video Lesson 19
NEW ! (August 2014) Prof. Barba is teaching a MOOC titled "Practical Numerical Methods with Python." Check it out:
http://openedx.seas.gwu.edu/courses/GW/MAE6286/2014_fall/about
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Nonlinear [...]convection—Inviscid Burgers’ equation, discretized with (iii) MacCormack scheme, (iv) Beam & Warming implicit method, and (v) Beam & Warming with artificial damping.
This video is part of the open courseware prepared by Prof. Lorena A. Barba.
For more, visit: http://lorenabarba.com
Follow: https://twitter.com/LorenaABarba
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ME 702 - Computational Fluid Dynamics - Video Lesson 17
NEW ! (August 2014) Prof. Barba is teaching a MOOC titled "Practical Numerical Methods with Python." Check it out:
http://openedx.seas.gwu.edu/courses/GW/MAE6286/2014_fall/about
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Spectral analysis of numerical [...]schemes III — Analysis of Lax-Friedrichs: amplitudes strongly damped for smaller values of CFL number; no diffusion error at phase angle=180º explains odd-even decoupling (error oscillation of wavelength 2 mesh widths); dispersion error always greater than 1 (leading phase error). Analysis Lax-Wendroff: large range of phase angles with very low diffusion error; dispersion error mostly lagging type. Analysis of leapfrog: it has no diffusion errors (i.e., leapfrog scheme is particularly useful in long-term simulations, e.g., long weather forecasts); dispersion error is of lagging type; neutral stability can cause problems, as high-frequency errors will not be damped. Leaprog is not recommended for high-speed flows where shocks can occur! Presentation of the explicit Beam-Warming method, using second-order backward-difference (upwind) scheme. Analysis of Beam-Warming: wide region of accuracy with respect to diffusion error; dispersion error greater than one (oscillations move ahead of solution). Final note: a key quantity is the number of mesh points per wavelength.
This video is part of the open courseware prepared by Prof. Lorena A. Barba.
For more, visit: http://lorenabarba.com
Follow: https://twitter.com/LorenaABarba
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ME 702 - Computational Fluid Dynamics - Video Lesson 16
NEW ! (August 2014) Prof. Barba is teaching a MOOC titled "Practical Numerical Methods with Python." Check it out:
http://openedx.seas.gwu.edu/courses/GW/MAE6286/2014_fall/about
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Spectral analysis of numerical [...]schemes II — Error analysis for hyperbolic problems: 1D linear advection. “Leading errorâ€: numerical convection faster than physical; “lagging errorâ€: numerical convection slower than physical.
This video is part of the open courseware prepared by Prof. Lorena A. Barba.
For more, visit: http://lorenabarba.com
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ME 702 - Computational Fluid Dynamics - Video Lesson 13
NEW ! (August 2014) Prof. Barba is teaching a MOOC titled "Practical Numerical Methods with Python." Check it out:
http://openedx.seas.gwu.edu/courses/GW/MAE6286/2014_fall/about
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New schemes for convection [...](including stencil and von Neumann stability): (1) Leapfrog (2) Lax-Friedrichs (3) Lax-Wendroff
This video is part of the open courseware prepared by Prof. Lorena A. Barba.
For more, visit: http://lorenabarba.com
Follow: https://twitter.com/LorenaABarba
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ME 702 - Computational Fluid Dynamics - Video Lesson 12
NEW ! (August 2014) Prof. Barba is teaching a MOOC titled "Practical Numerical Methods with Python." Check it out:
http://openedx.seas.gwu.edu/courses/GW/MAE6286/2014_fall/about
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Steps 9 to 12 of the [...]Navier-Stokes programming assignment. (Step 9) Laplace equation, (Step 10) Poisson equation, (Step 11) Navier-Stokes case 1, “cavityâ€; (Step 12) Navier-Stokes case 2, “channelâ€.
This video is part of the open courseware prepared by Prof. Lorena A. Barba.
For more, visit: http://lorenabarba.com
Follow: https://twitter.com/LorenaABarba
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ME 702 - Computational Fluid Dynamics - Video Lesson 11
NEW ! (August 2014) Prof. Barba is teaching a MOOC titled "Practical Numerical Methods with Python." Check it out:
http://openedx.seas.gwu.edu/courses/GW/MAE6286/2014_fall/about
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Computation of the [...]Navier-Stokes equations for incompressible flow: there is no obvious way to couple velocity and pressure; take the divergence of the momentum and use continuity to get a Poisson equation for pressure.
This video is part of the open courseware prepared by Prof. Lorena A. Barba.
For more, visit: http://lorenabarba.com
Follow: https://twitter.com/LorenaABarba
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