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Gradients-Limiters.md

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title Gradients and Limiters
permalink /docs_v7/Gradients-Limiters/

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.

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 (edge-based).
  • WEIGHTED_LEAST_SQUARES: Compute the gradient of a field using inverse-distance-weighted approximation. The default value is WEIGHTED_LEAST_SQUARES.

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.

Thin Shear Layer gradient reconstruction is always used for the construction of the Jacobian.

Limiters

SU2 implements limiter functions to prevent the generation of oscillations when using second order 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, with reference length of 1.
  • VENKATAKRISHNAN_WANG : Slope limiter using Venkatakrisnan method, with a small non-vanishing bias proportional to the min-to-max range of the solution, to avoid limiting in small regions.
  • 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 VENKATAKRISHNAN being the default option.

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 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 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.

The value of the limiter can be frozen after a certain amount of iterations, which can be specified in the LIMITER_ITER. The default value is $999999$.