[FLASH-USERS] Hybrid Riemann solver in USM

[Yi-Hao Chen]

Hi Dongwook, <ychen at astro.wisc.edu>

Thank you very much for the useful information, especially the relevant
section in your paper and the crash course.

These help a lot!

Yi-Hao


On Thu, Jul 26, 2018 at 11:55 AM Dongwook Lee <dongwook at flash.uchicago.edu>
wrote:

> Dea Yi-Hao,
>
> Thanks for pointing out the inconsistency on the information. This
> happened mainly because various parts of the code go through more frequent
> updates than the users manual.
>
> I'd like to let you know that this inconsistency doesn't really matter too
> much though, as far as the code combines two different Riemann solvers
> depending on the local shock strength information.
> What is important here is to combine a sophisticated Riemann solver (e.g.,
> Roe, HLLD, or HLLC) on smooth cells and a robust solver (HLL or a local
> Lax-Friedrichs (LLF)) on shock cells.
>
> If you want to know why you would need this, please see Section 4.6 in my
> paper, Lee, JCP, 243 (2013).
>
> In addition, if you want to learn more about general Riemann solvers, the
> FLASH users manual is not good enough. You should find better references
> such as the famous book by Toro, "Riemann solvers and numerical methods for
> fluid dynamics: a practical introduction". Also, there are numerous papers
> you can read too. You can easily find some key papers if you search
> keywords like HLL-type of Riemann solvers, Roe solvers, Godunov methods,
> and so on. You may also follow the references in Toro as well as my JCP
> paper.
>
> I am sure you will enjoy learning all these mathematical algorithms on
> such novel Riemann solvers, but I am also happy to give you a one-line
> crash course as well -- Among the Riemann solvers that FLASH implements,
> you have:
>
> More wave structures (less stable) <----------> Less wave structures (more
> stable)
>
>    - For MHD:  Roe > HLLD > HLL ~ LLF
>    - For Hydro: Roe ~ HLLC > HLL ~ LLF
>
> Now you see clearly what the strategy of a hybrid Riemann solver needs to
> be. You can combine any two different types of Riemann solvers to balance
> accuracy and stability, otherwise, some numerical instabilities (e.g.,
> carbuncle instability, see the discussion in Lee, JCP, 243 (2013)) can
> happen and may crash your run. There is another approach to improve Riemann
> solvers using *multi-dimensional* formulations. See various studies by
> Balsara, Dumbser, etc. (e.g., JCP, 261 (2014)).
>
> Hope this helps,
> Dongwook
>
>
>
> On Wed, Jul 25, 2018 at 4:57 PM Yi-Hao Chen <ychen at astro.wisc.edu> wrote:
>
>> Dear All,
>>
>> I found there is some inconsistency between the manual and the code in
>> describing the hybrid Riemann solver in unsplit staggered mesh scheme.
>>
>> In the user manual, section 14.3.3, it says "A hybrid type of Riemann
>> solver which combines using the Roe solver for high accuracy and HLLD for
>> stability is also available."
>>
>> However, in the source code, choosing the hybrid Riemann solver will call
>> HLL solver for shock region and call HLLD (MHD) or HLLC (hydro) solver
>> otherwise. The code I refer to is located in
>> source/physics/Hydro/HydroMain/unsplit/hy_uhd_getFaceFlux.F90
>> I believe this is the only place in the code that chooses different
>> Riemann solvers. Please let me know if there are somewhere else.
>>
>> The version that I have been using is FLASH 4.4, but I checked version
>> 4.5 and the same description is still there.
>>
>> Another related question is: how do people choose which solver to use?
>> The FLASH user manual has a good description of the Roe solver, but very
>> little on all other available solvers. I understand this is probably not an
>> easy question to answer. But it would be very helpful if someone can point
>> out resources that introduce or compare different Riemann solvers.
>> Especially what solvers are suitable for what kind of problem and maybe the
>> cautions of using a particular solver.
>>
>> Thank you!
>>
>> Best,
>> Yi-Hao
>>
>>
>>
>
> =========================================
> Dongwook Lee, Ph.D., Associate Professor
> Applied Mathematics
> University of California, Santa Cruz
> Baskin Engineering, Room 353C
> 1156 High Street, Santa Cruz, CA 95064
> https://users.soe.ucsc.edu/~dongwook/
>
>
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