A Finite Element/Neural Network Framework for Modeling Suspensions of Non-spherical Particles

Becker, R., Braack, M.: Multigrid techniques for finite elements on locally refined meshes. Numer. Linear Algebra Appl. 7, 363–379 (2000)

Becker, R., Braack, M.: A finite element pressure gradient stabilization for the Stokes equations based on local projections. Calcolo 38, 173–199 (2001)

Becker, R., Braack, M.: A two-level stabilization scheme for the navier-stokes equations. In: Feistauer, M., Dolejší, V., Knobloch, P., Najzar, K (eds.) Numerical Mathematics and Advanced Applications, ENUMATH 2003, pp 123–130. Springer, Berline, Heidelberg (2004)

Becker, R, Braack, M, Meidner, D, Richter, T, Vexler, B: The finite element toolkit Gascoigne. https://www.gascoigne.de (2005)

Braack, M., Burman, E., John, V., Lube, G.: Stabilized finite element methods for the generalized Oseen problem. Comput. Methods Appl. Mech. Eng. 196, 853–866 (2007)

Chhabra, R.P., Agarwal, L., Sinha, N.K.: Drag on non-spherical particles: an evaluation of available methods. Powder Technol. 101, 288–295 (1999)

Clift, R., Grace, J., Weber, M.: Bubbles, Drops, and Particles. Academic Press, New York (1978)

Failer, L., Minakowski, P., Richter, T.: On the impact of fluid structure interaction in blood flow simulations. Vietnam J Math. https://doi.org/10.1007/s10013-020-00456-6 (2020)

Failer, L., Richter, T.: A Newton multigrid framework for optimal control of fluid–structure interactions. Optim Eng. https://doi.org/10.1007/s11081-020-09498-8 (2020)

Failer, L., Richter, T.: A parallel Newton multigrid framework for monolithic fluid-structure interactions. J. Sci. Comput. 82, 28 (2020)

Fasano, A., Sequeira, A.: Blood coagulation. In: Hemomath, pp. 79–158. Springer International Publishing, Cham (2017)

Filipovic, N., Kojic, M., Tsuda, A.: Modelling thrombosis using dissipative particle dynamics method. Philos. Trans. R. Soc. Ser. A 366, 3265–3279 (2008)

Fogelson, A.L., Guy, R.D.: Immersed-boundary-type models of intravascular platelet aggregation. Comput. Methods Appl. Mech. Eng. 197, 2087–2104 (2008)

Heywood, J., Rannacher, R.: Finite-element approximation of the nonstationary Navier–Stokes problem. Part IV: Error analysis for second-order time discretization. SIAM J. Number. Anal. 27, 353–384 (1990)

Heywood, J., Rannacher, R., Turek, S.: Artificial boundaries and flux and pressure conditions for the incompressible Navier-Stokes equations. Int. J. Numer. Methods Fluids 22, 325–352 (1996)

Hartmann, D., Lessig, C., Margenberg, N., Richter, T.: A neural network multigrid solver for the Navier–Stokes equations. arXiv:2008.11520 (2020)

Hölzer, A., Sommerfeld, M.: New simple correlation formula for the drag coefficient of non-spherical particles. Powder Technol. 184, 361–365 (2008)

Hölzer, A., Sommerfeld, M.: Lattice Boltzmann simulations to determine drag, lift and torque acting on non-spherical particles. Comput. Fluids 38, 572–589 (2009)

Kimmritz, M., Richter, T.: Parallel multigrid method for finite element simulations of complex flow problems on locally refined meshes. Numer. Linear Algebra Appl. 18, 615–636 (2010)

Fogelson, A.L., Neeves, K.B.: Fluid mechanics of blood clot formation. Ann. Rev. Fluid Mech. 47, 377–403 (2015)

Lu, G., Third, J., Müller, C.: Discrete element models for non-spherical particle systems: from theoretical developments to applications. Chem. Eng. Sci. 127, 425–465 (2015)

Luding, S.: Collisions & contacts between two particles. In: Herrmann, H. J., Hovi, J. -P., Luding, S (eds.) Physics of Dry Granular Media. NATO ASI Series, Vol. 350, pp. 285–304. Springer, Dordrecht (1998)

Mandø, M., Rosendahl, L.: On the motion of non-spherical particles at high Reynolds number. Powder Technol. 202, 1–13 (2010)

Mody, N.A., King, M.R.: Three-dimensional simulations of a platelet-shaped spheroid near a wall in shear flow. Phys. Fluids 17, 113302 (2005)

Muth, B., Müller, M. -K., Müller, M. K., Eberhard, P., Luding, S.: Collision detection and administration methods for many particles with different sizes. In: Cleary, P. (ed.) Discrete Element Methods, DEM 07, 4th International Conference on Discrete Element Methods, DEM 4 - Brisbane, Australia, pp. 1–18. Minerals Engineering Int. (2007)

Ouchene, R., Khalij, M., Arcen, B., Tanière, A.: A new set of correlations of drag, lift and torque coefficients for non-spherical particles and large reynolds numbers. Powder Technol. 303, 33–43 (2016)

Ouchene, R., Khalij, M., Tanière, A., Arcen, B.: Drag, lift and torque coefficients for ellipsoidal particles: From low to moderate particle Reynolds numbers. Comput. Fluids 113, 53–64 (2015)

Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chintala, S.: Pytorch: An imperative style, high-performance deep learning library. In: Wallach, H., Larochelle, H., Beygelzimer, A., d’Alché Buc, F., Fox, E., Garnett, R (eds.) Advances in Neural Information Processing Systems 32, pp. 8024–8035. Curran Associates, Inc (2019)

Plimpton, S.: Fast parallel algorithms for short-range molecular dynamics. J. Comput. Phys. 117, 1–19 (1995)

Richter, T.: Fluid-structure Interactions. Models, Analysis and Finite Elements. Lecture Notes in Computational Science and Engineering, vol. 118. Springer, Cham, Berlin (2017)

Rosendahl, L.: Using a multi-parameter particle shape description to predict the motion of non-spherical particle shapes in swirling flow. Appl. Math. Model. 24, 11–25 (2000)

Saad, Y.: Iterative Methods for Sparse Linear Systems. PWS Publishing Company (1996)

Sanjeevi, S., Kuipers, J., Padding, J.: Drag, lift and torque correlations for non-spherical particles from Stokes limit to high Reynolds numbers. Int. J. Multiph. Flow 106, 325–337 (2018)

Shardt, O., Derksen, J.: Direct simulations of dense suspensions of non-spherical particles. Int. J. Multiph. Flow 47, 25–36 (2012)

Sweet, C.R., Chatterjee, S., Xu, Z., Bisordi, K., Rosen, E.D., Alber, M.: Modelling platelet-blood flow interaction using the subcellular element Langevin method. J. R. Soc. Interface 8, 1760–1771 (2011)

Tosenberger, A., Ataullakhanov, F., Bessonov, N., Panteleev, M., Tokarev, A., Volpert, V.: Modelling of thrombus growth in flow with a DPD-PDE method. J. Theor. Bio. 337, 30–41 (2013)

Viallat, A., Abkarian, M.: Dynamics of Blood Cell Suspensions in Microflows. CRC Press, Boca Raton (2019)

Wadell, H.: The coefficient of resistance as a function of Reynolds number for solids of various shapes. J. Franklin Inst. 217, 459–490 (1934)

Wiwanitkit, V.: Plateletcrit, mean platelet volume, platelet distribution width: Its expected values and correlation with parallel red blood cell parameters. Clin. Appl. Thromb./Hemost. 10, 175–178 (2004)

Xu, Z., Chen, N., Kamocka, M., Rosen, E., Alber, M.: A multiscale model of thrombus development. J. R. Soc. Interface 5, 705–22 (2008)

Xu, Z., Chen, N., Shadden, S.C., Marsden, J.E., Kamocka, M.M., Rosen, E.D., Alber, M.: Study of blood flow impact on growth of thrombi using a multiscale model. Soft Matter 5, 769–779 (2009)

Xu, Z., Lioi, J., Mu, J., Kamocka, M.M., Liu, X., Chen, D.Z., Rosen, E.D., Alber, M.: A multiscale model of venous thrombus formation with surface-mediated control of blood coagulation cascade. Biophys. J. 98, 1723–1732 (2010)

Yan, S., He, Y., Tang, T., Wang, T.: Drag coefficient prediction for non-spherical particles in dense gas–solid two-phase flow using artificial neural network. Powder Technol. 354, 115–124 (2019)

Yow, H., Pitt, M., Salman, A.: Drag correlations for particles of regular shape. Adv. Powder Technol. 16, 363–372 (2005)

Zastawny, M., Mallouppas, G., Zhao, F., van Wachem, B.: Derivation of drag and lift force and torque coefficients for non-spherical particles in flows. Int. J. Multiph. Flow 39, 227–239 (2012)

Zhang, P., Gao, C., Zhang, N., Slepian, M., Deng, Y., Bluestein, D.: Multiscale particle-based modeling of flowing platelets in blood plasma using dissipative particle dynamics and coarse grained molecular dynamics. Cel. Mol. Bioeng. 7, 552–574 (2014)

von Wahl, H., Richter, T., Frei, S., Hagemeier, T.: Falling balls in a viscous fluid with contact: Comparing numerical simulations with experimental data. arXiv:2011.08691 (2020)

Zhong, W., Yu, A., Liu, X., Tong, Z., Zhang, H.: DEM/CFD-DEM Modelling of non-spherical particulate systems: Theoretical developments and applications. Powder Technol. 302, 108–152 (2016)

Zhu, H., Zhou, Z., Yang, R., Yu, A.: Discrete particle simulation of particulate systems: Theoretical developments. Chem. Eng. Sci. 62, 3378–3396 (2007)

Zhu, H., Zhou, Z., Yang, R., Yu, A.: Discrete particle simulation of particulate systems: a review of major applications and findings. Chem. Eng. Sci. 63, 5728–5770 (2008)