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Limiter function in TVD schemes

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Old   August 27, 2008, 12:34
Default Hello all, I'm trying to im
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Maria Magdalena Poschner
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Hello all,

I'm trying to implement real gas behaviour into OpenFOAM and at the moment I'm just checking the code for any occurence of the speed of sound as a variable affecting the flux limiter calculated for the TVD Schemes. As I would have to change the formulation if it is calculated directly within the routine which calculates the flux limiter.

I think there would be only an effect if any spectral radius is concerned in the flux limiter, as it is done in some approaches. May be there any model which accounts for the speed of sound for limiting the flux and I didn't find it?


If there is any effect, where can I find it?

Thanks for a lot!

Maria Magdalena
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Old   August 28, 2008, 12:36
Default Hello all, I need some help
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Maria Magdalena Poschner
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Hello all,

I need some help in understanding what is done in the Convective Differencing Scheme in combination with a TVD scheme in OpenFOAM.

I read Hrovje Jasak's Ph. D thesis and according to that I think I found out that the upwards and central differencing scheme used for the TVD schemes are always Beam and Warming and Lax-Wendroff. I hope I did get that correctly.

To my knowledge for a Lax-Wendroff scheme there has a Jacobi-matrix to be calculated. Up to now I couldn't find out where this matrix is calculated, but it would be very important for me to know what exactly is programmed to avoid that there is any influence of a change in the equation of state which has to be taken into account directly in there. Is it possible that there is no effect at all, as the pressure gradient term is no part of the convective term?

As a second, I'm wondering if there is any spectral radius accounted for in the Beam and Warming Scheme. If there is one, it should depend on the speed of sound, which is defined as a pressure derivative by the density. Dependent on the calculation it might have to be modified, but I also didn't find where it is calculated in OpenFOAM.

May be anyone could give me a refernce for how the described calculations are done in OpenFOAM and perhaps give me a hint where I have to look in the code for the calculation of the Jacobian and the Eigenvalues.

Thanks a lot and best regards,

Maria Magdalena
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Old   August 28, 2008, 15:59
Default Hi Maria, First of all, Beam
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M. Mahdi Salehi
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Hi Maria,
First of all, Beam & Warming and Lax-Wendroff schemes have nothing to do with TVD schemes. Read part 1.2.1 of Hrv's thesis completely.
After that, in OpenFOAM the convective terms are linearized by lagging the flux; not by calculating Jacobian matrices. Read part 3.8, specifically page 144. Therefore, no equation of state is involved in solving the momentum equation.
Good luck,
Mahdi
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