Update documentation for Gradients and Limiters #83
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Included a section dedicated only to the gradients and limiters.
suargi
commented
Jun 30, 2022
| - `WALL_DISTANCE` : Slope limiter based on wall distance. | ||
| With the `VENKATAKRISHNAN` being the default option. | ||
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| The `VENKAT_LIMITER_COEFF` tunable field is used to compute the small non-vanishing bias to prevent divisions by zero, $\epsilon$. Depending on the limiter to be used this field has different interpretations. For the `VENKATAKRISHNAN` limiter it represents the constant $K$ in $\epsilon^2=\left(K\Delta x\right)^3$. We refer to [Venkatakrishnan](https://doi.org/10.1006/jcph.1995.1084) for further details. For the `VENKATAKRISHNAN_WANG` limiter it represents the constant $\epsilon^{\prime}$ in $\epsilon = \epsilon^{\prime}(q^{\text{\max}}-q^{\text{\min}})$. We refer to [Wang](https://doi.org/10.2514/6.1996-2091) for further details. For both limiters larger values of `VENKAT_LIMITER_COEFF` decrease the extent of limiting, while values approaching zero cause lower-order approximation to the solution. Larger values of `VENKAT_LIMITER_COEFF` will reduce the high frequency oscillations of the sulition making it more stable and attaining better convergence properties. On expense, the accuracy of the solution will be typycally affected. The dafault value is 0.05. |
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I have written the last part: "Larger values of VENKAT_LIMITER_COEFF will..." based on theory and my experience. Please correct it/me in case it is wrong.
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It's a bit misleading. Specify that the oscillations are of the residuals (aka flip flopping).
More limiting can make convergence more difficult. But not enough limiting can make the solver diverge. It's a trade-off and it needs tuning. For example a finer mesh for the same problem needs a smaller value to be completely consistent.
pcarruscag
reviewed
Jun 30, 2022
| permalink: /docs_v7/Gradients-Limiters/ | ||
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| This page lists the gradient of the space computation methods and the limiter functions in SU2 as well as their associated options, it is not meant as a detailed theory guide but some application guidance is given nonetheless. The options listed here do not apply to the high order DG solver. |
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The start of this sentence is not very clear.
| - `VENKATAKRISHNAN_WANG` : Slope limiter using Venkatakrisnan method, with the small non-vanishing bias to prevent divisions by zero based on the min-to-max range of the solution. | ||
| - `BARTH_JESPERSEN` : Slope limiter using Barth-Jespersen method. | ||
| - `VAN_ALBADA_EDGE` : Slope limiter using Van Albada method. | ||
| - `SHARP_EDGES` : Slope limiter based on the distance to the nearest sharp edge. |
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This and wall distance should not be used for flow solvers
| - `WALL_DISTANCE` : Slope limiter based on wall distance. | ||
| With the `VENKATAKRISHNAN` being the default option. | ||
|
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| The `VENKAT_LIMITER_COEFF` tunable field is used to compute the small non-vanishing bias to prevent divisions by zero, $\epsilon$. Depending on the limiter to be used this field has different interpretations. For the `VENKATAKRISHNAN` limiter it represents the constant $K$ in $\epsilon^2=\left(K\Delta x\right)^3$. We refer to [Venkatakrishnan](https://doi.org/10.1006/jcph.1995.1084) for further details. For the `VENKATAKRISHNAN_WANG` limiter it represents the constant $\epsilon^{\prime}$ in $\epsilon = \epsilon^{\prime}(q^{\text{\max}}-q^{\text{\min}})$. We refer to [Wang](https://doi.org/10.2514/6.1996-2091) for further details. For both limiters larger values of `VENKAT_LIMITER_COEFF` decrease the extent of limiting, while values approaching zero cause lower-order approximation to the solution. Larger values of `VENKAT_LIMITER_COEFF` will reduce the high frequency oscillations of the sulition making it more stable and attaining better convergence properties. On expense, the accuracy of the solution will be typycally affected. The dafault value is 0.05. |
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Adapt the divisions by zero according to my comment above, the true purpose is not to prevent div by 0
| - `WALL_DISTANCE` : Slope limiter based on wall distance. | ||
| With the `VENKATAKRISHNAN` being the default option. | ||
|
|
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| The `VENKAT_LIMITER_COEFF` tunable field is used to compute the small non-vanishing bias to prevent divisions by zero, $\epsilon$. Depending on the limiter to be used this field has different interpretations. For the `VENKATAKRISHNAN` limiter it represents the constant $K$ in $\epsilon^2=\left(K\Delta x\right)^3$. We refer to [Venkatakrishnan](https://doi.org/10.1006/jcph.1995.1084) for further details. For the `VENKATAKRISHNAN_WANG` limiter it represents the constant $\epsilon^{\prime}$ in $\epsilon = \epsilon^{\prime}(q^{\text{\max}}-q^{\text{\min}})$. We refer to [Wang](https://doi.org/10.2514/6.1996-2091) for further details. For both limiters larger values of `VENKAT_LIMITER_COEFF` decrease the extent of limiting, while values approaching zero cause lower-order approximation to the solution. Larger values of `VENKAT_LIMITER_COEFF` will reduce the high frequency oscillations of the sulition making it more stable and attaining better convergence properties. On expense, the accuracy of the solution will be typycally affected. The dafault value is 0.05. |
There was a problem hiding this comment.
It's a bit misleading. Specify that the oscillations are of the residuals (aka flip flopping).
More limiting can make convergence more difficult. But not enough limiting can make the solver diverge. It's a trade-off and it needs tuning. For example a finer mesh for the same problem needs a smaller value to be completely consistent.
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Thank you for continuing this work, it's good info 👍 |
Co-authored-by: Pedro Gomes <[email protected]>
Co-authored-by: Pedro Gomes <[email protected]>
Co-authored-by: Pedro Gomes <[email protected]>
Co-authored-by: Pedro Gomes <[email protected]>
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Included a section dedicated only to gradients and limiters.
This pull request complements #81.