An Efficient B-Spline Lagrangian/Eulerian Method for Compressible Flow, Shock Waves, and Fracturing Solids

Cao, Yadi; Chen, Yunuo; Li, Minchen; Yang, Yin; Zhang, Xinxin; Aanjaneya, Mridul; Jiang, Chenfanfu

doi:10.1145/3519595

Title: An Efficient B-Spline Lagrangian/Eulerian Method for Compressible Flow, Shock Waves, and Fracturing Solids

Journal Article · 13 May 2022 · ACM Transaction on Graphics

DOI: https://doi.org/10.1145/3519595 · OSTI ID:2423962

^[1];

^[2]; Zhang, Xinxin ^[3]; Aanjaneya, Mridul ^[4]; Jiang, Chenfanfu ^[1]

Univ. of California, Los Angeles, CA (United States)
Clemson Univ., SC (United States)
Zenus Technology, Shenzhen Guangdong (China)
Rutgers Univ., Piscataway, NJ (United States)

This study presents a new method for modeling the interaction between compressible flow, shock waves, and deformable structures, emphasizing destructive dynamics. Extending advances in time-splitting compressible flow and the Material Point Methods (MPM), we develop a hybrid Eulerian and Lagrangian/Eulerian scheme for monolithic flow-structure interactions. We adopt the second-order WENO scheme to advance the continuity equation. To stably resolve deforming boundaries with sub-cell particles, we propose a blending treatment of reflective and passable boundary conditions inspired by the theory of porous media. The strongly coupled velocity-pressure system is discretized with a new mixed-order finite element formulation employing B-spline shape functions. Shock wave propagation, temperature/density-induced buoyancy effects, and topology changes in solids are unitedly captured.

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Research Organization:: Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)

Sponsoring Organization:: USDOE; National Science Foundation (NSF)

Grant/Contract Number:: AC05-00OR22725

OSTI ID:: 2423962

Journal Information:: ACM Transaction on Graphics, Journal Name: ACM Transaction on Graphics Journal Issue: 5 Vol. 41; ISSN 0730-0301

Publisher:: Association for Computing Machinery (ACM)Copyright Statement

Country of Publication:: United States

Language:: English

References (45)

Weighted Essentially Non-oscillatory Schemes Liu, Xu-Dong; Osher, Stanley; Chan, Tony Journal of Computational Physics, Vol. 115, Issue 1 https://doi.org/10.1006/jcph.1994.1187	journal	November 1994
A Higher-Order Boundary Treatment for Cartesian-Grid Methods Forrer, Hans; Jeltsch, Rolf Journal of Computational Physics, Vol. 140, Issue 2 https://doi.org/10.1006/jcph.1998.5891	journal	March 1998
Multidimensional Upwinding. Part II. Decomposition of the Euler Equations into Advection Equations Fey, Michael Journal of Computational Physics, Vol. 143, Issue 1 https://doi.org/10.1006/jcph.1998.5959	journal	June 1998
Flip: A low-dissipation, particle-in-cell method for fluid flow Brackbill, J. U.; Kothe, D. B.; Ruppel, H. M. Computer Physics Communications, Vol. 48, Issue 1 https://doi.org/10.1016/0010-4655(88)90020-3	journal	January 1988
Application of a particle-in-cell method to solid mechanics Sulsky, Deborah; Zhou, Shi-Jian; Schreyer, Howard L. Computer Physics Communications, Vol. 87, Issue 1-2 https://doi.org/10.1016/0010-4655(94)00170-7	journal	May 1995
Efficient implementation of essentially non-oscillatory shock-capturing schemes Shu, Chi-Wang; Osher, Stanley Journal of Computational Physics, Vol. 77, Issue 2 https://doi.org/10.1016/0021-9991(88)90177-5	journal	August 1988
A multidimensional generalization of Roe's flux difference splitter for the euler equations Deconinck, H.; Roe, P. L.; Struijs, R. Computers & Fluids, Vol. 22, Issue 2-3 https://doi.org/10.1016/0045-7930(93)90053-C	journal	March 1993
Numerical simulation of the interaction between a nonlinear elastic structure and compressible flow by the discontinuous Galerkin method Kosík, Adam; Feistauer, Miloslav; Hadrava, Martin Applied Mathematics and Computation, Vol. 267 https://doi.org/10.1016/j.amc.2015.02.057	journal	September 2015
Fluid–structure interaction solver for compressible flows with applications to blast loading on thin elastic structures Bailoor, Shantanu; Annangi, Aditya; Seo, Jung Hee Applied Mathematical Modelling, Vol. 52 https://doi.org/10.1016/j.apm.2017.05.038	journal	December 2017
A coupled finite volume and material point method for two-phase simulation of liquid–sediment and gas–sediment flows Baumgarten, Aaron S.; Couchman, Benjamin L. S.; Kamrin, Ken Computer Methods in Applied Mechanics and Engineering, Vol. 384 https://doi.org/10.1016/j.cma.2021.113940	journal	October 2021
A non-staggered coupling of finite element and lattice Boltzmann methods via an immersed boundary scheme for fluid-structure interaction Li, Zhe; Favier, Julien Computers & Fluids, Vol. 143 https://doi.org/10.1016/j.compfluid.2016.11.008	journal	January 2017
Visual simulation of shockwaves Sewall, Jason; Galoppo, Nico; Tsankov, Georgi Graphical Models, Vol. 71, Issue 4 https://doi.org/10.1016/j.gmod.2009.03.002	journal	July 2009
A method for avoiding the acoustic time step restriction in compressible flow Kwatra, Nipun; Su, Jonathan; Grétarsson, Jón T. Journal of Computational Physics, Vol. 228, Issue 11 https://doi.org/10.1016/j.jcp.2009.02.027	journal	June 2009
Numerically stable fluid–structure interactions between compressible flow and solid structures Grétarsson, Jón Tómas; Kwatra, Nipun; Fedkiw, Ronald Journal of Computational Physics, Vol. 230, Issue 8 https://doi.org/10.1016/j.jcp.2011.01.005	journal	April 2011
A conservative coupling algorithm between a compressible flow and a rigid body using an Embedded Boundary method Monasse, L.; Daru, V.; Mariotti, C. Journal of Computational Physics, Vol. 231, Issue 7 https://doi.org/10.1016/j.jcp.2012.01.002	journal	April 2012
Fully conservative leak-proof treatment of thin solid structures immersed in compressible fluids Grétarsson, Jón Tómas; Fedkiw, Ron Journal of Computational Physics, Vol. 245 https://doi.org/10.1016/j.jcp.2013.02.017	journal	July 2013
A monolithic mass tracking formulation for bubbles in incompressible flow Aanjaneya, Mridul; Patkar, Saket; Fedkiw, Ronald Journal of Computational Physics, Vol. 247 https://doi.org/10.1016/j.jcp.2013.03.048	journal	August 2013
A cut-cell finite volume – finite element coupling approach for fluid–structure interaction in compressible flow Pasquariello, Vito; Hammerl, Georg; Örley, Felix Journal of Computational Physics, Vol. 307 https://doi.org/10.1016/j.jcp.2015.12.013	journal	February 2016
An angular momentum conserving affine-particle-in-cell method Jiang, Chenfanfu; Schroeder, Craig; Teran, Joseph Journal of Computational Physics, Vol. 338 https://doi.org/10.1016/j.jcp.2017.02.050	journal	June 2017
An immersed boundary method for fluid–structure interaction with compressible multiphase flows Wang, Li; Currao, Gaetano M. D.; Han, Feng Journal of Computational Physics, Vol. 346 https://doi.org/10.1016/j.jcp.2017.06.008	journal	October 2017
A unified approach to monolithic solid-fluid coupling of sub-grid and more resolved solids Hyde, David A. B.; Fedkiw, Ronald Journal of Computational Physics, Vol. 390 https://doi.org/10.1016/j.jcp.2019.03.049	journal	August 2019
A general fluid–sediment mixture model and constitutive theory validated in many flow regimes Baumgarten, Aaron S.; Kamrin, Ken Journal of Fluid Mechanics, Vol. 861 https://doi.org/10.1017/jfm.2018.914	journal	December 2018
On the Boussinesq Approximation for a Compressible Fluid. Spiegel, E. A.; Veronis, G. The Astrophysical Journal, Vol. 131 https://doi.org/10.1086/146849	journal	March 1960
The numerical solution of the Navier-Stokes equations for an incompressible fluid Chorin, Alexandre Joel Bulletin of the American Mathematical Society, Vol. 73, Issue 6 https://doi.org/10.1090/S0002-9904-1967-11853-6	journal	January 1967
Fast Fluid Simulations with Sparse Volumes on the GPU Wu, Kui; Truong, Nghia; Yuksel, Cem Computer Graphics Forum, Vol. 37, Issue 2 https://doi.org/10.1111/cgf.13350	journal	May 2018
A Hybrid Lagrangian/Eulerian Collocated Velocity Advection and Projection Method for Fluid Simulation Gagniere, S.; Hyde, D.; Marquez‐Razon, A. Computer Graphics Forum, Vol. 39, Issue 8 https://doi.org/10.1111/cgf.14096	journal	November 2020
Animating suspended particle explosions Feldman, Bryan E.; O'Brien, James F.; Arikan, Okan ACM SIGGRAPH 2003 Papers on - SIGGRAPH '03 https://doi.org/10.1145/1201775.882336	conference	January 2003
A fast variational framework for accurate solid-fluid coupling Batty, Christopher; Bertails, Florence; Bridson, Robert ACM Transactions on Graphics, Vol. 26, Issue 3 https://doi.org/10.1145/1276377.1276502	journal	July 2007
Procedural fluid modeling of explosion phenomena based on physical properties Kawada, Genichi; Kanai, Takashi Proceedings of the 2011 ACM SIGGRAPH/Eurographics Symposium on Computer Animation https://doi.org/10.1145/2019406.2019429	conference	August 2011
A material point method for snow simulation Stomakhin, Alexey; Schroeder, Craig; Chai, Lawrence ACM Transactions on Graphics, Vol. 32, Issue 4 https://doi.org/10.1145/2461912.2461948	journal	July 2013
Augmented MPM for phase-change and varied materials Stomakhin, Alexey; Schroeder, Craig; Jiang, Chenfanfu ACM Transactions on Graphics, Vol. 33, Issue 4 https://doi.org/10.1145/2601097.2601176	journal	July 2014
SPGrid: a sparse paged grid structure applied to adaptive smoke simulation Setaluri, Rajsekhar; Aanjaneya, Mridul; Bauer, Sean ACM Transactions on Graphics, Vol. 33, Issue 6 https://doi.org/10.1145/2661229.2661269	journal	November 2014
The material point method for simulating continuum materials Jiang, Chenfanfu; Schroeder, Craig; Teran, Joseph ACM SIGGRAPH 2016 Courses https://doi.org/10.1145/2897826.2927348	conference	July 2016
Stable fluids Stam, Jos Proceedings of the 26th annual conference on Computer graphics and interactive techniques - SIGGRAPH '99 https://doi.org/10.1145/311535.311548	conference	January 1999
A polynomial particle-in-cell method Fu, Chuyuan; Guo, Qi; Gast, Theodore ACM Transactions on Graphics, Vol. 36, Issue 6 https://doi.org/10.1145/3130800.3130878	journal	November 2017
A moving least squares material point method with displacement discontinuity and two-way rigid body coupling Hu, Yuanming; Fang, Yu; Ge, Ziheng ACM Transactions on Graphics, Vol. 37, Issue 4 https://doi.org/10.1145/3197517.3201293	journal	July 2018
Animating fluid sediment mixture in particle-laden flows Gao, Ming; Pradhana, Andre; Han, Xuchen ACM Transactions on Graphics, Vol. 37, Issue 4 https://doi.org/10.1145/3197517.3201309	journal	August 2018
Efficient and conservative fluids using bidirectional mapping Qu, Ziyin; Zhang, Xinxin; Gao, Ming ACM Transactions on Graphics, Vol. 38, Issue 4 https://doi.org/10.1145/3306346.3322945	journal	July 2019
CD-MPM: continuum damage material point methods for dynamic fracture animation Wolper, Joshuah; Fang, Yu; Li, Minchen ACM Transactions on Graphics, Vol. 38, Issue 4 https://doi.org/10.1145/3306346.3322949	journal	July 2019
AnisoMPM Wolper, Joshuah; Chen, Yunuo; Li, Minchen ACM Transactions on Graphics, Vol. 39, Issue 4 https://doi.org/10.1145/3386569.3392428	journal	August 2020
Iq-Mpm Fang, Yu; Qu, Ziyin; Li, Minchen ACM Transactions on Graphics, Vol. 39, Issue 4 https://doi.org/10.1145/3386569.3392438	journal	August 2020
A massively parallel and scalable multi-GPU material point method Wang, Xinlei; Qiu, Yuxing; Slattery, Stuart R. ACM Transactions on Graphics, Vol. 39, Issue 4 https://doi.org/10.1145/3386569.3392442	journal	July 2020
Scene mover Wang, Hanqing; Liang, Wei; Yu, Lap-Fai ACM Transactions on Graphics, Vol. 39, Issue 6 https://doi.org/10.1145/3414685.3417788	journal	November 2020
Bijective and coarse high-order tetrahedral meshes Jiang, Zhongshi; Zhang, Ziyi; Hu, Yixin ACM Transactions on Graphics, Vol. 40, Issue 4 https://doi.org/10.1145/3450626.3459840	journal	August 2021
A General Technique for Eliminating Spurious Oscillations in Conservative Schemes for Multiphase and Multispecies Euler Equations Fedkiw, R.; Liu, X. -D.; Osher, S. International Journal of Nonlinear Sciences and Numerical Simulation, Vol. 3, Issue 2 https://doi.org/10.1515/IJNSNS.2002.3.2.99	journal	January 2002

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