Modeling of the 3D unsteady multiscale multiphase fluid flow with shocks: Numerical methods and implementation algorithms
- 1 Keldysh Institute of Applied Mathematics RAS, Moscow, Russian Federation
Abstract
Numerical simulation is widely applied in the fluid dynamic research. Unsteady multiphase flow with high Mach and Reynolds numbers has high physical and mathematical fidelity and a special approach of its correct modeling is required. In this paper the appropriate numerical methods and special algorithms of implementation are developed for high-performance numerical modeling using the modern computational systems. The results of validation tasks and problems of practical importance are presented.
Keywords
References
- Flow simulation and high performance computing / T. Tezduyar [et al.] // Computational Mechanics. –– 1996. –– Vol. 18, no. 6. –– Pp. 397––412.
- Geller T. Supercomputing’s exaflop target // Communications of the ACM. –– 2011. –– Vol. 54, no. 8. –– Pp. 16––18.
- Nickolls J., Dally W. J. The GPU Computing Era // IEEE Micro. –– 2010. –– Vol. 30, no. 2. –– Pp. 56––69.
- Hagen T. R., Lie K.-A., Natvig J. R. Solving the Euler equations on graphics processing units // International Conference on Computational Science. –– Springer. 2006. –– Pp. 220––227.
- Brodtkorb A. R., Hagen T. R., Sætra M. L. Graphics processing unit (GPU) programming strategies and trends in GPU computing // Journal of Parallel and Distributed Computing. –– 2013. –– Vol. 73, no. 1. –– Pp. 4––13. Metaheuristics on GPUs.
- Batchelor G. K. An introduction to fluid dynamics. – Cambridge university press, 2000.
- Abgrall R. How to prevent pressure oscillations in multicomponent flow calculations: a quasi conservative approach // Journal of Computational Physics. – 1996. – V. 125. – No. 1. – P. 150-160.
- Cockburn B., Shu C.-W. The local discontinuous Galerkin method for timedependent convection-diffusion systems // SIAM Journal on Numerical Analysis. –– 1998. –– Vol. 35, no. 6. –– Pp. 2440––2463.
- Toro E. Riemann Solvers and Numerical Methods for Fluid Dynamics: A Practical Introduction. –– Springer, 2009.
- Krivodonova L. Limiters for high-order discontinuous Galerkin methods // Journal of Computational Physics. –– 2007. –– Vol. 226, no. 1. –– Pp. 879––896.
- Moe S. A., Rossmanith J. A., Seal D. C. A simple and effective high-order shock-capturing limiter for discontinuous Galerkin methods // arXiv preprint arXiv:1507.03024. –– 2015.
- Levchenko V. D., Perepelkina A. Y. Locally recursive nonlocally asynchronous algorithms for stencil computation // Lobachevskii Journal of Mathematics. – 2018. – V. 39. – No. 4. – P. 552-561.
- Korneev B. A., Levchenko V. D. Simulating threedimensional unsteady viscous compressible flow on GPU using the DiamondTorre algorithm // Preprints of the Keldysh Institute of Applied Mathematics. – 2018. – . 105-17.
- Korneev B., Levchenko V. Numerical simulation of increasing initial perturbations of a bubble in the bubble–shock interaction problem // Fluid Dynamics Research. – 2016. – V. 48. – No. 6. – P. 061412.
- Hinze J. Fundamentals of the hydrodynamic mechanism of splitting in dispersion processes // AIChE Journal. –– 1955. –– Vol. 1, no. 3. –– Pp. 289––295.
- Taylor G. The shape and acceleration of a drop in a high speed air stream // The scientific papers of GI Taylor. –– 1963. –– Vol. 3. –– Pp. 457––464.
- Secondary breakup of a drop at moderate Weber numbers / M. Jain [et al.] // Proc. R. Soc. A. –– 2015. –– Vol. 471, no. 2177. – – P. 20140930.