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Surpassing Boundaries in Fluid Dynamics Using the Smoothed Particle Hydrodynamics–Continuous Boundary Force Method

In the paper, “Smoothed Particle Hydrodynamics Continuous Boundary Force Method for Navier-Stokes Equations Subject to a Robin Boundary Condition,” published in the Journal of Computational Physics, lead author Wenxiao Pan, the CM4 project task leader for Scalable Algorithms and Applications (from Pacific Northwest National Laboratory), and her co-authors introduce and evaluate a new method—smoothed particle hydrodynamics-continuous boundary force (SPH-CBF)—to analyze and model physical phenomena associated with fluid flows and the forces that affect them at various scales and boundary conditions. The SPH-CBF formulation has several advantages for solving Navier-Stokes equations. Most notably, the SPH discretization of the equations and boundary condition that results from the CBF method offer a computationally efficient way to model boundary conditions ranging from no slip to full slip.

To examine its accuracy, the SPH-CBF method was tested with two- and three-dimensional plane shear flow, as well as a periodic lattice of cylinders. The results then were compared with those obtained using finite difference or finite element method (FEM) approaches. Even in a domain with complex boundaries, comparisons of SPH-CBF velocity profiles closely agreed with those from the FEM solutions, demonstrating the method’s capability for modeling flows with different slip lengths.

In addition to advancing existing SPH theory, the method uses SPH strengths in modeling diverse physics problems, such as those involving atmospheric systems, energy materials and processes, subsurface flow and transport, and high-strength materials, which are highly relevant to important U.S. Department of Energy mission objectives (see related highlight).

The research was conducted through the CM4 project supported by DOE’s Office of Advanced Scientific Computing Research Applied Mathematics program.

Reference: Pan W, J Bao, and AM Tartakovsky. 2014. “Smoothed Particle Hydrodynamics Continuous Boundary Force Method for Navier-Stokes Equations Subject to a Robin Boundary Condition.” Journal of Computational Physics 259:242-259. DOI: 10.1016/j.jcp.2013.12.014.

A New Way to get the Temperature Right: The Fluctuating Hydrodynamics Thermostat

Recently published in Physical Review E, "Dynamic implicit-solvent coarse-grained models of lipid bilayer membranes: Fluctuating hydrodynamics thermostat," is co-authored by Paul J. Atzberger, a co-principal investigator with the CM4 project from the University of California, Santa Barbara. The work introduces a momentum-conserving fluctuating hydrodynamics thermostat for dynamic simulations of implicit-solvent coarse-grained models, which addresses important correlations and dynamic contributions that standard implicit-solvent models and Langevin dynamics approaches can overlook.

The fluctuating hydrodynamics thermostat couples coarse-grained degrees of freedom to a stochastic continuum field that accounts for both the solvent hydrodynamics and thermal fluctuations. In their work, the scientists investigated the diffusivity of lipids within the bilayer and their spatial correlations. Their results revealed lipid motions exhibit interesting collective correlations, resembling a vortex-like flow structure similar to those observed in other explicit solvent bilayer simulations. Thus, the fluctuating hydrodynamics thermostat captures important solvent-mediated effects not accounted for in conventional Langevin dynamics. The results also indicate that introduced fluctuating hydrodynamics methods provides a promising set of approaches for extending implicit-solvent lipid models for studies of dynamical phenomena within lipid bilayer membranes.

The research was supported by several grants from the National Science Foundation, as well as the Collaboratory on Mathematics for Mesoscopic Modeling of Materials (CM4) sponsored by the Department of Energy's Office of Advanced Scientific Computing Research.

Reference: Wang Y, JK Sigurdsson, E Brandt, and PJ Atzberger. 2013. "Dynamic implicit-solvent coarse-grained models of lipid bilayer membranes: Fluctuating hydrodynamics thermostat." Physical Review E 88(2):023301. DOI: 10.1103/PhysRevE.88.023301

Mesoscale Simulations See into Sickle Cells

The research of Dr. George Karniadakis, a joint appointee at PNNL and Brown University and principal investigator of the CM4 project, was recently referenced in The Telegraph (U.K.) in an article about how computer programs are being used to create lifelike models of the human body (http://bit.ly/1bSFmdC). Dr. Karniadakis' research involved using a systematic, dissipative particle dynamics-based (a stochastic simulation technique for complex fluids) simulation study of individual sickle red blood cells in shear flow to analyze the biophysical characteristics surrounding vasoocclusion crisis, vascular blockage that occurs when sickle-shaped cells obstruct circulation.

The research was supported by the National Institutes of Health and the Collaboratory on Mathematics for Mesoscopic Modeling of Materials (CM4) sponsored by the Department of Energy's Office of Advanced Scientific Computing Research. Computations were made possible via an ASCR Innovative & Novel Computational Impact on Theory and Experiment (INCITE) award.

Reference: Lei H and GE Karniadakis. 2013. "Probing vasoocclusion phenomena in sickle cell anemia via mesoscopic simulations." Proceedings of the National Academy of Sciences (PNAS) 110(28):11326-11330. DOI: 10.1073/pnas.1221297110.

 

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