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[WIP] Add documentation #59
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--- | ||
title: Gradients and Limiters | ||
permalink: /docs_v7/Gradients-Limiters/ | ||
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This page lists the gradient 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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## Gradient Computation ## | ||
The numerical method for the computation of the spatial gradients used for viscous fluxes and source terms is specified by the `NUM_METHOD_GRAD` field. The list of available options is given below. | ||
`GREEN_GAUSS`: Classic gradient reconstruction based on the Green-Gauss theorem. | ||
`WEIGHTED_LEAST_SQUARES`: Compute the gradient of a field using inverse-distance-weighted approximation. | ||
The default option is set to `WEIGHTED_LEAST_SQUARES`. | ||
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The spatial gradients method used only for upwind reconstruction is specified by the `NUM_METHOD_GRAD_RECON` field. An additional method is available; `LEAST_SQUARES`: Compute the gradient of a field using unweighted Least- Squares approximation. If the `NUM_METHOD_GRAD_RECON` field is left empty or set to `NONE` it defaults to `NUM_METHOD_GRAD`. | ||
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Thin Shear Layer gradient reconstruction is always used for the construction of the Jacobian. | ||
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## Limiters ## | ||
SU2 implements limiter functions to prevent the generation of oscillations when using upwind spatial discretisations. These are specified by the config field `SLOPE_LIMITER_FLOW`. The available options are: | ||
- `NONE` - No limiter | ||
- `VENKATAKRISHNAN` - Slope limiter using Venkatakrisnan method. | ||
- `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. | ||
- `WALL_DISTANCE` - Slope limiter based on wall distance. | ||
With the default option set to `VENKATAKRISHNAN`. | ||
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The `VENKAT_LIMITER_COEFF` 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. The dafault value is 0.05. | ||
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The option `LIMITER_ITER` specifies the number of iterations afterFreeze the value of the limiter after a number of iterations. DEFAULT value $999999$. |
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That would be "fluxes" theory.
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You are right in the sense that the Jacobian construction belongs to a "fluxes" section. However the discussion on which gradient computation method is used for its construction might belong to the "Gradients" section.