Numerical Simulation of Planar Moving Shock Interacting with a Single Row of Water Columns and Multi-material Interfaces

doi:10.19596/j.cnki.1001-246x.7635

Abstract

Abstract: A moving planar shock interacting with multi-material interfaces in compressible fluid on fixed Descartes grids is studied. Level-set method combined with a revised real ghost fluid method(rGFM) are applied for tracking gas-water and gas-solid interfaces, where a revised Riemann problem is constructed and its approximate solutions are populated for real and ghost fluid status. WENO schemes are employed for Euler and level-set equations. Numerical schlieren images are obtained for demonstrating shock evolution. Complex shock structures distinguish accurately and show various interfaces embedded in the fluid. Other than partition and coordinate transformation, we offer an approach for computation of complex flow field on Descartes grids involving multi-material interfaces or objects.

Key words: planar shock, interface, WENO schemes, level-set, GFM

CLC Number:

ZHAO Qi, ZHANG Mengping, XU Shengli, LU Jianfang. Numerical Simulation of Planar Moving Shock Interacting with a Single Row of Water Columns and Multi-material Interfaces[J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2018, 35(3): 285-293.

References

[1] CHEN H, LIANG S M. Flow visualization of shock/water column interactions[J]. Shock Waves, 2008, 17(5):309-321.
[2] JIA Z P, SUN Y T. A 2D cell-centered MMALE method based on MOF interface reconstruction[J]. Chinese Journal of Computational Physics, 2016, 33(5):523-538.
[3] ZHOU J, XU S L. Numerical inlet and outlet boundary conditions in SPH method[J].Chinese J Comput Phys,2016,33(5):516-522.
[4] FEDKIW R P, ASLAM T, MERRIMAN B, et al. A non-oscillatory Eulerian approach to interfaces in multimaterial flows (the ghost fluid method)[J]. Journal of Computational Physics, 1999, 152(2):457-492.
[5] FEDKIW R P, MARQUINA A, MERRIMAN B. An isobaric fix for the overheating problem in multimaterial compressible flows[J]. Journal of Computational Physics, 1999, 148(2):545-578.
[6] FEDKIW R P. Coupling an Eulerian fluid calculation to a Lagrangian solid calculation with the ghost fluid method[J]. Journal of Computational Physics, 2002, 175(1):200-224.
[7] LIU T G, KHOO B C, YEO K S. Ghost fluid method for strong shock impacting on material interface[J]. Journal of Computational Physics, 2003, 190(2):651-681.
[8] WANG C W, LIU T G, KHOO B C. A real ghost fluid method for the simulation of multimedium compressible flow[J]. SIAM Journal on Scientific Computing, 2006, 28(1):278-302.
[9] SAMBASIVAN S K, UDAYKUMAR H S. Sharp interface simulations with local mesh refinement for multi-material dynamics in strongly shocked flows[J]. Computers & Fluids, 2010, 39(9):1456-1479.
[10] JIANG L, GE H, FENG C L, et al. Numerical simulation of underwater explosion bubble with a refined interface treatment[J]. Science China:Physics, Mechanics & Astronomy, 2015, 58(4):1-10.
[11] 徐爽. 大密度比水气多介质问题数值模拟与高阶DSD方法研究[D]. 南京:南京航空航天大学, 2014.
[12] 徐爽, 赵宁, 王春武,等. 水/气多介质问题的界面处理方法[J]. 爆炸与冲击, 2015, 35(3):326-334.
[13] ALLAIRE G, CLERC S, KOKH S. A five-equation model for the simulation of interfaces between compressible fluids[J]. Journal of Computational Physics, 2002, 181(2):577-616.
[14] SAMBASIVAN S K, UDAYKUMAR H S. Ghost fluid method for strong shock interactions Part 1:Fluid-fluid interfaces[J]. AIAA Journal, 2009, 47(12):2907-2922.
[15] SAMBASIVAN S K, UDAYKUMAR H S. Ghost fluid method for strong shock interactions Part 2:Immersed solid boundaries[J]. AIAA Journal, 2009, 47(12):2923-2937.
[16] SAUREL R, ABGRALL R. A simple method for compressible multifluid flows[J]. SIAM Journal on Scientific Computing, 1999, 21(3):1115-1145.
[17] OSHER S, FEDKIW R P. Level set methods:An overview and some recent results[J]. Journal of Computational Physics, 2001, 169(2):463-502.
[18] LIU X D, OSHER S, CHAN T. Weighted essentially non-oscillatory schemes[J]. Journal of Computational Physics, 1994, 115(1):200-212.
[19] JIANG G S, SHU C W. Efficient implementation of weighted ENO schemes[R]. Institute for Computer Applications in Science and Engineering, Hampton VA, 1995.
[20] JIANG G S, PENG D. Weighted ENO schemes for Hamilton-Jacobi equations[J]. SIAM Journal on Scientific Computing, 2000, 21(6):2126-2143.
[21] SHU C W. High order weighted essentially nonoscillatory schemes for convection dominated problems[J]. SIAM Review, 2009, 51(1):82-126.
[22] SHU C W. Essentially non-oscillatory and weighted essentially non-oscillatory schemes for hyperbolic conservation laws[M]//Advanced Numerical Approximation of Nonlinear Hyperbolic Equations. Springer Berlin Heidelberg, 1998:325-432.
[23] GOTTLIEB S, SHU C W. Total variation diminishing Runge-Kutta schemes[J]. Mathematics of Computation of the American Mathematical Society, 1998, 67(221):73-85.
[24] 赵琪. 激波和界面相互作用的数值研究[D].合肥:中国科学技术大学,2017.