# Viscous interface: ldg-beta and ldg-tau definition

**URL:** <https://pyfr.discourse.group/t/viscous-interface-ldg-beta-and-ldg-tau-definition/1117>\
**Category:** Cases\
**Tags:** config\
**Created:** [30 June 2024 17:33 UTC](https://pyfr.discourse.group/t/viscous-interface-ldg-beta-and-ldg-tau-definition/1117 "2024-06-30T17:33:53Z")\
**Posts on this page:** 7\
**Page:** 1

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**Author:** ![Frankx9](https://avatars.discourse-cdn.com/v4/letter/f/3e96dc/32.png) [@Frankx9](https://pyfr.discourse.group/u/Frankx9)\
**Post date:** [30 June 2024 17:33 UTC](https://pyfr.discourse.group/t/viscous-interface-ldg-beta-and-ldg-tau-definition/1117/1 "2024-06-30T17:33:54Z")

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Hello,

where may I find more informations regarding ldg-beta and ldg-tau in the literature? Could you point to a good reference to study them?

Best regards

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**Author:** ![fdw](https://avatars.discourse-cdn.com/v4/letter/f/a587f6/32.png) [@fdw](https://pyfr.discourse.group/u/fdw)\
**Post date:** [1 July 2024 09:17 UTC](https://pyfr.discourse.group/t/viscous-interface-ldg-beta-and-ldg-tau-definition/1117/2 "2024-07-01T09:17:06Z")

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See Eq (25) and (27) in:

[https://www.sciencedirect.com/science/article/pii/S0010465514002549](https://www.sciencedirect.com/science/article/pii/S0010465514002549)

along with the references therein.

Regards, Freddie.

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**Author:** ![Frankx9](https://avatars.discourse-cdn.com/v4/letter/f/3e96dc/32.png) [@Frankx9](https://pyfr.discourse.group/u/Frankx9)\
**Post date:** [1 July 2024 10:25 UTC](https://pyfr.discourse.group/t/viscous-interface-ldg-beta-and-ldg-tau-definition/1117/3 "2024-07-01T10:25:05Z")

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Thanks a lot for the answer, very grateful

Best regards

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<div class="post-metadata">

**Author:** ![Frankx9](https://avatars.discourse-cdn.com/v4/letter/f/3e96dc/32.png) [@Frankx9](https://pyfr.discourse.group/u/Frankx9)\
**Post date:** [3 July 2024 12:16 UTC](https://pyfr.discourse.group/t/viscous-interface-ldg-beta-and-ldg-tau-definition/1117/4 "2024-07-03T12:16:32Z")

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Hi @fdw,

is there any relationship in terms of accuracy of the computed solution if the values are not 0.5 and 0.1 respectively? E.g. ldg-tau = 1,2 … or ldg-beta any other value in [-1, 1]?

Best regards

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**Author:** ![fdw](https://avatars.discourse-cdn.com/v4/letter/f/a587f6/32.png) [@fdw](https://pyfr.discourse.group/u/fdw)\
**Post date:** [3 July 2024 21:50 UTC](https://pyfr.discourse.group/t/viscous-interface-ldg-beta-and-ldg-tau-definition/1117/5 "2024-07-03T21:50:54Z")

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The differences are typically minor. Taking `ldg-beta` to be \pm 0.5 does have slight performance advantages hence it is the default.

Regards, Freddie.

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<div class="post-metadata">

**Author:** ![Frankx9](https://avatars.discourse-cdn.com/v4/letter/f/3e96dc/32.png) [@Frankx9](https://pyfr.discourse.group/u/Frankx9)\
**Post date:** [3 July 2024 22:02 UTC](https://pyfr.discourse.group/t/viscous-interface-ldg-beta-and-ldg-tau-definition/1117/6 "2024-07-03T22:02:12Z")

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To my understanding for ldc-beta ± 0.5 is because of upwind/downwind biasing with a compact stencil (am I right?) but what about tau? Is any value “reasonable” with minor deteriorations even large ones like 1.0, 2.0 etc…?

Best regards

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<div class="post-metadata">

**Author:** ![fdw](https://avatars.discourse-cdn.com/v4/letter/f/a587f6/32.png) [@fdw](https://pyfr.discourse.group/u/fdw)\
**Post date:** [6 July 2024 06:13 UTC](https://pyfr.discourse.group/t/viscous-interface-ldg-beta-and-ldg-tau-definition/1117/7 "2024-07-06T06:13:36Z")

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The performance benefit comes from the fact that when beta is \pm 1/2 that you only need gradients from one side of the interface. This reduces the amount of work that the common interface flux code has to perform.

Larger values of `ldg-tau` may introduce excessive dissipation and there is not usually a benefit to using anything outside the range of zero to one.

Regards, Freddie.