Accurate and efficient splitting methods for dissipative particle dynamics

We study numerical methods for dissipative particle dynamics (DPD), which is a system of stochastic differential equations and a popular stochastic momentum-conserving thermostat for simulating complex hydrodynamic behavior at mesoscales. We propose a new splitting method that is able to substantially improve the accuracy and efficiency of DPD simulations in a wide range of the friction coefficients, particularly in the extremely large friction limit that corresponds to a fluid-like Schmidt number, a key issue in DPD. Various numerical experiments on both equilibrium and transport properties are performed to demonstrate the superiority of the newly proposed method over popular alternative schemes in the literature

Smoothed particle hydrodynamics and its applications for multiphase flow and reactive transport in porous media

Smoothed particle hydrodynamics (SPH) is a Lagrangian method based on a meshless discretization of partial differential equations. In this review, we present SPH discretization of the Navier-Stokes and advection-diffusion-reaction equations, implementation of various boundary conditions, and time integration of the SPH equations, and we discuss applications of the SPH method for modeling pore-scale multiphase flows and reactive transport in porous and fractured media.United States. Dept. of Energy. Office of Advanced Scientific Computing Research (Early Career Award, “New Dimension Reduction Methods and Scalable Algorithms for Multiscale Nonlinear Phenomena,” and Collaboratory on Mathematics for Mesoscopic Modeling of Materials (CM4)

Numerical modeling of microfluidic through the smoothed particle hydrodynamics mesh-free lagrangian method

Orientador: Luiz Otávio Saraiva FerreiraTese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia MecânicaResumo: O transporte controlado de pequenas quantidades de fluidos é fundamental para desenvolver os laboratórios químicos em um chip (Lab-On-a-Chip, ou LOC, em inglês), ou seja, sistemas miniaturizados de crescente utilização na análise em áreas como Química, Bioquímica, Farmácia e Biologia, que tendem a substituir os atuais equipamentos analíticos. Os microdispositivos são essenciais para o transporte controlado e preciso de fluidos. Porém, ainda não foi desenvolvida uma metodologia para o cálculo do comportamento de fluidos em micro-dispositivos, existindo assim uma demanda por modelos numéricos capazes de realizá-lo. Esse trabalho apresenta a implementação do método sem malha Smoothed Particle Hydrodynamics (SPH) no desenvolvimento de um simulador 2D para problemas de escoamento de fluidos em micro-dispositivos. O simulador foi programado na linguagem C/C++ para processamento em CPU e na linguagem CUDA-C para processamento em GPU. O estudo da formulação SPH incluiu fenômenos como tensão superficial, multi-fase, capilaridade e molhabilidade para problemas com interação fluido-fluido e fluido-estrutura. As etapas de desenvolvimento do simulador computacional foram: Revisão de métodos de partículas Lagrangianos sem malha elegíveis para a modelagem da interação fluido-estrutura em micro-sistemas; Metologia e formulação das equações constitutivas para a descrição do comportamento do fluido, da estrutura e da interação fluido-estrutura usando SPH; Implementação de fenômenos caraterísticos para micro-fluídica como multi-fase (líquido-líquido) e tensão superficial e capilaridade; E modelagem numérica de microdispositivos para caso de estudo em micro-válvulas e micro-bomba peristáltica. Todas as implementações das formulações no simulador foram validadas através da comparação com resultados da literatura e da experimentação. Assim, o principal objetivo desse trabalho é apresentar o método SPH como uma alternativa na modelagem numérica de fluidos com interação líquido-líquido e líquido-estrutura em problemas de micro-fluídicaAbstract: Controlled transport of small amounts of fluids is critical for Lab-On-a-Chip, miniaturized systems of increasing use of chemical, biochemical, pharmaceutical and biological analyzes that tend to replace current analytical equipment. Micro-Devices are essential for controlled and accurate transport of fluids. However, a methodology for the calculation of fluid behavior in micro-devices has not yet been developed, and there is a demand for capable numerical models. This work presents the implementation of the Smoothed Particle Hydrodynamics (SPH) meshless method in the development of a 2D simulator for fluid flow problems in micro-devices. The simulator was programmed in the C/C++ language for CPU processing and CUDA-C language for GPU processing. The study of SPH formulation included phenomena such as surface tension, multi-phase, capillarity and wettability between fluid-fluid and fluid-structure. The steps of development of the computational simulator were: Review of non-mesh lagrangean particle methods eligible for modeling of fluid-structure interaction in micro-systems; Metology and formulation of constitutive equations for the description of fluid, structure and fluid-structure behavior using SPH; Implementation of micro-fluidic phenomena such as multi-phase (liquid-liquid) and surface tension and capillarity. All implementations of formulations and simulator validated by comparing results in literature and experimentation. Thus, the main objective of this work was to demonstrate SPH as a tool in the numerical modeling of fluids in liquid-liquid interaction and liquid-structure for the problems involved in microfluidic and micro-devicesDoutoradoMecanica dos Sólidos e Projeto MecanicoDoutor em Engenharia Mecânica2012/21090-5FAPES

Simulation of micro-scale porous flow using Smoothed Particle Hydrodynamics

Fluid flow in a porous medium is a well-studied aspect of applied mathematics with significant real-world application. The standard modelling approach for this type of flow is to homogenise the porous structure. A dual-scale model, with the smaller scale at the pore-scale, would possibly capture the fluid mechanical phenomena more faithfully than a volume averaged approach. We investigate the significance of the microstructure shape on the flux through the medium. We also evaluate whether smoothed particle hydrodynamics may be viable in a dual-scale model. We find that varying the shape of the porous structure causes the average flux to vary significantly. This contradicts the assumption commonly made that only the porosity is important. We conclude that there is significant information present in the dual-scale model that is lost by a volume averaged model. We also find that the smoothed particle hydrodynamics simulation is computationally intensive, but that there is a time-saving measure that may provide viability to the dual-scale model. References S. Alyaev, E. Keilegavlen, and J. M. Nordbotten. Analysis of control volume heterogeneous multiscale methods for single phase flow in porous media. Multiscale Model. Sim., 12(1):335–363, 2014. doi:10.1137/120885541 H. Brenner. Dispersion resulting from flow through spatially periodic porous media. Phil. Trans. R. Soc. A, 297(1430):81–133, 1980. doi:10.1098/rsta.1980.0205 L. Brookshaw. A method of calculating radiative heat diffusion in particle simulations. Proc. Astron. Soc. Aust., 6(2):207–210, 1985. http://adsabs.harvard.edu/abs/1985PASAu...6..207B. E. J. Carr and I. W. Turner. Two-scale computational modelling of water flow in unsaturated soils containing irregular-shaped inclusions. Int. J. Numer. Meth. Eng., 98(3):157–173, 2014. doi:10.1002/nme.4625 A. J. Chorin. A numerical method for solving incompressible viscous flow problems. J. Comput. Phys., 2(1):12–26, 1967. doi:10.1016/0021-9991(67)90037-X R. A. Gingold and J. J. Monaghan. Smoothed particle hydrodynamics: Theory and application to non-spherical stars. Mon. Not. R. Astron. Soc., 181:375–389, 1977. doi:10.1093/mnras/181.3.375 S. Litvinov, M. Ellero, X. Y. Hu, and N. A. Adams. A splitting scheme for highly dissipative smoothed particle dynamics. J. Comput. Phys., 229(15):5457–5464, 2010. doi:10.1016/j.jcp.2010.03.040 L. B. Lucy. A numerical approach to the testing of the fission hypothesis. Astron. J., 82(12):1013–1024, 1977. doi:10.1086/112164 C. C. Mei, J. L. Auriault, and C.-O. Ng. Some applications of the homogenization theory. Adv. Appl. Mech., 32:278–348, 1996. doi:10.1016/S0065-2156(08)70078-4 J. J. Monaghan. Smoothed particle hydrodynamics. Annu. Rev. Astron. Astrophys., 30:543–574, 1992. doi:10.1146/annurev.aa.30.090192.002551 J. J. Monaghan. Implicit SPH drag and dusty gas dynamics. J. Comput. Phys., 138(2):801–820, 1997. doi:10.1006/jcph.1997.5846 J. J. Monaghan. From stars to volcanoes: The SPH story. In Eduardo Ramos, Gerardo Cisneros, Rafael Fernandez-Flores, and Alfredo Santillan-Gonzalez, editors, Computational Fluid Dynamics, Proceedings of the Fourth UNAM Supercomputing Conference, pages 193–203, Singapore, 2001. World Scientific. doi:10.1142/4623 J. J. Monaghan. Smoothed particle hydrodynamics. Rep. Prog. Phys., 68:1703–1759, 2005. doi:10.1088/0034-4885/68/8/R01 J. P. Morris. A study of the stability properties of smooth particle hydrodynamics. Publ. Astron. Soc. Aust., 13:97–102, 1996. http://adsabs.harvard.edu/abs/1996PASA...13...97M. J. P. Morris, P. J. Fox, and Y. Zhu. Modeling low Reynolds number incompressible flows using SPH. J. Comput. Phys., 136(1):214–226, 1997. doi:10.1006/jcph.1997.5776 D. J. Price. Smoothed particle hydrodynamics and magnetohydrodynamics. J. Comput. Phys., 231(3):759–794, 2012. doi:10.1016/j.jcp.2010.12.011 S. Shao and E. Y. M. Lo. Incompressible SPH method for simulating Newtonian and non-Newtonian flows with a free surface. Adv. Water Resour., 26(7):787–800, 2003. doi:10.1016/S0309-1708(03)00030-7 R. E. Showalter. Microstructure models of porous media. In Homogenization and Porous Media, pages 183–202. Interdisciplinary Applied Mathematics. Springer New York, 1997. doi:10.1007/978-1-4612-1920-0_9 A. Szymkiewicz, J. Lewandowska, R. Angulo-Jaramillo, and J. Butlariska. Two-scale modeling of unsaturated water flow in a double-porosity medium under axisymmetric conditions. Can. Geotech. J., 45:238–251, 2008. doi:10.1139/T07-096 P. van Liedekerke, B. Smeets, T. Odenthal, E. Tijskens, and H. Ramon. Solving microscopic flow problems using Stokes equations in SPH. Comput. Phys. Commun., 184:1686–1696, 2013. doi:10.1016/j.cpc.2013.02.013 S. Whitaker. Flow in porous media I: A theoretical derivation of Darcy's law. Transport Porous Med., 1(1):3–25, 1986. doi:10.1007/BF01036523 S. Whitaker. Coupled transport in multiphase systems: A theory of drying. Adv. Heat Trans., 31:1–104, 1998. doi:10.1016/S0065-2717(08)70240-