Abstract
We introduce a new kinetic model where the equilibrium distribution function has a range of velocities centered about two velocities (\(\pm \lambda \)) in 1D. In 2D, the equilibrium distribution comprises of a range of velocities about four velocities, one in each quadrant. This essential feature of a range of velocities (\(\lambda \pm \Delta \lambda \)) offers a significant advantage to obtain both an exact shock capturing as well as an entropic scheme. The range of velocities (2\(\Delta \lambda \)) serves the purpose of augmenting the stability of the model. \(\Delta \lambda \) is used to provide additional diffusion in expansion regions. The average velocity \(\lambda \) is fixed to exactly capture grid-aligned steady discontinuities, by enforcing Rankine-Hugoniot jump conditions in the discretization process. Further, a novel kinetic relative entropy, appropriate to our kinetic model, is introduced. Along with an additional criterion, this kinetic relative entropy is used to identify expansions. Some standard 1D and 2D benchmark test cases are solved using this scheme.
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References
Aregba-Driollet, D., Natalini, R.: Discrete kinetic schemes for multidimensional systems of conservation laws. SIAM J. Numer. Anal. 37(6), 1973–2004 (2000)
Bhatnagar, P.L., Gross, E.P., Krook, M.: A model for collision processes in gases. I. small amplitude processes in charged and neutral one-component systems. Phys. Rev. 94(3), 511 (1954)
Bouchut, F.: Construction of BGK models with a family of kinetic entropies for a given system of conservation laws. J. Stat. Phys. 95(1), 113–170 (1999)
Gottlieb, S., Shu, C.W., Tadmor, E.: Strong stability-preserving high-order time discretization methods. SIAM Rev. 43(1), 89–112 (2001)
Venkatakrishnan, V.: On the accuracy of limiters and convergence to steady state solutions. In: 31st Aerospace Sciences Meeting, p. 880 (1993)
Zaide, D., Roe, P.: Entropy-based mesh refinement, II: a new approach to mesh movement. In: 19th AIAA Computational Fluid Dynamics, p. 3791 (2009)
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Roy, S.S., Raghurama Rao, S.V. (2024). An Entropic Kinetic Scheme with Compactly Supported Velocities. In: Parés, C., Castro, M.J., Morales de Luna, T., Muñoz-Ruiz, M.L. (eds) Hyperbolic Problems: Theory, Numerics, Applications. Volume II. HYP 2022. SEMA SIMAI Springer Series, vol 35. Springer, Cham. https://doi.org/10.1007/978-3-031-55264-9_37
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DOI: https://doi.org/10.1007/978-3-031-55264-9_37
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