Blast wave simulations using Euler equations and adaptive grids

Çözüm ağı noktalarını eşit-dağılım prensibine göre yeniden dağıtan bir intibak eden ağ metodu, patlama sonrası oluşan şok dalgalarını simule edebilen bir hesaplamalı akışkanlar dinamiği programına uygulanmıştır. Elde edilen program önce bir şok tüpü probleminde denenmiş ve akıştaki süreksizlikler güçlendikçe intibak edici ağları kullanmanın öneminin daha belirgin olduğu gözlemlenmiştir. Ayrıca akış değişkenlerini yeni ağ noktalarına taşıyan interpolasyon metodunun çözümlerin doğruluğunu direk etkilediği ve kütle korunumunu sağlamayan interpolasyon yöntemlerinin oldukça hatalı sonuçlar verdiği görülmüştür. Daha sonar yapılan patlama sonrası oluşan şok dalgası simülasyonları da, uygulanan intibak eden ağ yönteminin sonuçları, harcanan CPU zamanını çok fazla arttırmadan iyileştirdiğini göstermiştir.

Patlama sonrası oluşan şok dalgalarının Euler denklemleri ve intibak eden çözüm ağları kullanılarak simülasyonu

An adaptive grid method which redistributes grid points according to equidistribution principle was implemented to an in-house computational fluid dynamics code capable of simulating blast waves. The resultant code was first tested for a shock tube problem. It was observed that benefit of using adaptive grids becomes more evident when discontinuities in the flow are stronger. It was also observed that interpolation method used to move the flow variables to new grid locations directly affects the accuracy of the solution and interpolation methods which do not guarantee conservation of mass may yield highly inaccurate results. Blast wave simulations performed showed that the adaptive grid method used here improved predictions considerably without requiring a lot of extra CPU time.

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Alpman, E., Long, L, N., Chen, C. –C., Linzell, D. G., Prediction of Blast Loads on a Deformable Steel Plate Using Euler Equations, 18th AIAA Computational Fluid Dynamics Conference, Miami, FL, June 2007.
Alpman E., Simulation of Blast Waves using Euler Equations, 17th National Thermal Science and Technology Conference, Sivas, Turkey, June 2009. (in Turkish).
Anderson, J. B., Long, L. N., Direct Monte Carlo Simulation of Chemical Reaction Systems: Prediction of Ultrafast Detonations, Journal of Chemical Physics, 118 (7), 3102 – 311, 2003.
Anderson, J. B., Long, L. N., Direct Simulation of Pathological Detonations, 18th International Symposium on Rarefied Gas Dynamics, Vancouver, Canada, 2002.
Anderson, J. D. Modern Compressible Flow with Historical Perspective, 3rd Edition, McGraw Hill, 587, 2004.
Brode H. L., Numerical Solutions of Spherical Blast Waves, Journal of Applied Physics, 26 (6), 766 – 775, 1955.
Brode, H. L., Blast Wave from a Spherical Charge, The Physics of Fluids, 2 (2), 217 – 229, 1959.
Chen, C.C., Alpman, E., Linzell, D.G., and Long, L.N., Effectiveness of advanced coating systems for mitigating blast effects on steel components, Structures Under Shock and Impact X, Book Series: WIT Transactions on the Build Environment, 98, 85 - 94, 2008.
Chen, C.C., Linzell, D. G., Long, L. N., Alpman, E., Computational studies of polyurea coated steel plate under blast loads, 9th US National Congress on Computational Mechanics, San Francisco, CA, July 2007.
Dewey, J. M., Expanding Spherical Shocks (Blast Waves), Handbook of Shock Waves, 2, 441 – 481, 2001.
Dobratz, B. M., Crawford, P. C., LLNL Explosives Handbook – Properties of Chemical Explosives and Explosive Simulants, Lawrence Livermore National Laboratory, 1985.
Fritsch, F. N., Carlson, R. E., Monotone Piecewise Cubic Interpolation, SIAM Journal on Numerical Analysis, 17 (2), 238 – 246, 1980.
Hoffmann, K. A., Chiang, S. T., Computational Fluid Dynamics for Engineers, Volume I, Engineering Education SystemTM, 2004.
Hoffmann, K. A., Chiang, S. T., Siddiqui S., Papadakis, M., Fundamental Equations of Fluid Mechanics, Engineering Education SystemTM, 2002.
Hoffman, K., A., Chiang, S. T., Computational Fluid Dynamics, Volume II, Engineering Education SystemTM, 2000.
Hyde, D. W., CONWEP: Conventional Weapons Effects Program, US Army Waterways Experimental Station, 1991.a
Jones, H., Miller, A. R., The Detonation of Solid Explosives: The Equilibrium Conditions in the Detonation Wave-Front and the Adiabatic Expansion of the Products of Detonation, Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, 194, 490 – 507, 1948.
Kubota, S., Nagayama, K., Saburi, T., Ogata, Y., State Relations for a Two-Phase Mixture of Reacting explosives and Applications, Combustion and Flame, 74 – 84, 2007.
Liou, M. -S., A sequel to AUSM: AUSM+, Journal of Computational Physics, 129, 364 – 382, 1996.
Long, L. N, Anderson, J. B., The simulation of Detonations using a Monte Carlo Method, Rarefied Gas Dynamics Conference, Sydney, Australia, 2000.
Park, C., Nonequilibrium Hypersonic Aerothermodynamics, John-Wiley & Sons, Inc., 1990.
Roe, P. L., Characteristic-based Schemes for Euler Equations, Annual Review of Fluid Mechanics, 18, 337 – 365, 1986.
Sharma, A., Long, L. N., Numerical Simulation of the Blast Impact Problem using the Direct Simulation Monte Carlo (DSMC) Method, Journal of Computational Physics, 200, 211 – 237, 2004.
Smith, R. W., AUSM(ALE): A Geometrically conservative Arbitrary Lagrangian-Eulerian Flux Splitting Scheme, Journal of Computational Physics, 150, 268 – 286, 1999.
Smith, P. D., Hetherington J. D., Blast and Ballistic Loading of Structures, Butterworth-Heinemann, 24 – 62, 1994.
Sod, G. A., A survey of Several Finite Difference Methods for Systems of Nonlinear Hyperbolic Conservation Laws, Journal of Computational Physics 27 (1), 1 – 31, 1978.
Soni, B. K., Koomullil, R., Thompson, D. S., Thornburg, H., Solution Adaptive Grid Strategies Based on Point Redistribution, Computer Methods in Applied Mechanics and Engineering, 189, 1183 – 1204, 2000.
Tang, H., Tang, T., Adaptive Mesh Methods for Oneand Two-Dimensional Hyperbolic Conservation Laws, SIAM Journal of Numerical Analysis, 41 (2), 487 – 515, 2003.
Tannehill, J. C., Mugge P. H., Improved Curve Fits for the Thermodynamic Properties Equilibrium Air Suitable for Numerical Computation using Time Dependent and Shock-Capturing Methods, NASA CR-2470, 1974.
Tai, C. H., Chiang, D. C., Su, Y. P., Explicit Time Marching Methods for The Time-Dependent Euler Computations, Journal of Computational Physics, 130, 191 – 202, 1997.
Thornburg, H., Soni, B. K., Kishore, B., A Structured Grid Based Solution-Adaptive Technique for Complex Separated Flows, Applied Mathematics and Computation, 19, 259 – 273, 1998.
Van Dam, A., Zegeling, P. A., A Robust Moving Mesh Finite Volume Method Applied to 1D Hyperbolic Conservation Laws from Magnetohyrdodynamics, Journal of Computational Physics, 216, 526 – 546, 2006.
White, F. M., Fluid Mechanics, McGraw-Hill, 6th Edition, 17, 2006.