Bulletin of the American Physical Society
67th Annual Meeting of the APS Division of Fluid Dynamics
Volume 59, Number 20
Sunday–Tuesday, November 23–25, 2014; San Francisco, California
Session R31: CFD: Algorithms 
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Chair: Amir Riaz, University of Maryland Room: 2018 
Tuesday, November 25, 2014 1:05PM  1:18PM 
R31.00001: Dynamic Load Balancing Strategies for Parallel Reacting Flow Simulations Patrick Pisciuneri, Esteban Meneses, Peyman Givi Load balancing in parallel computing aims at distributing the work as evenly as possible among the processors. This is a critical issue in the performance of parallel, time accurate, flow simulators. The constraint of time accuracy requires that all processes must be finished with their calculation for a given time step before any process can begin calculation of the next time step. Thus, an irregularly balanced compute load will result in idle time for many processes for each iteration and thus increased walltimes for calculations. Two existing, dynamic load balancing approaches are applied to the simplified case of a partially stirred reactor for methane combustion. The first is Zoltan, a parallel partitioning, load balancing, and data management library developed at the Sandia National Laboratories. The second is Charm++, which is its own machine independent parallel programming system developed at the University of Illinois at UrbanaChampaign. The performance of these two approaches is compared, and the prospects for their application to full 3D, reacting flow solvers is assessed. [Preview Abstract] 
Tuesday, November 25, 2014 1:18PM  1:31PM 
R31.00002: Higherorder accurate asynchronytolerant schemes for CFD at extreme scales Aditya Konduri, Diego Donzis With increasing computational power, simulations of fluid flows are routinely being done on hundreds of thousands of processing elements (PE). At these extreme scales communication between PEs take a substantial amount of the total time. In future Exascale, communication time is likely to overwhelm computing time and affect the scalability. Our recent work on asynchronous method based on finitedifferences has shown the feasibility of carrying out computations in absence of data synchronization between PEs, reducing the communication time significantly. However, accuracy of commonly used schemes is affected and the error depends on the characteristics of the computing system. In this work, we develop new higherorder accurate schemes that are asynchronytolerant. We present a framework in which schemes with desired accuracy can be constructed taking into account machinespecific characteristics to trade off communication by memory or computation effort and quantitatively control the error introduced by asynchrony. We design schemes, prove their properties using model equations and evaluate their performance uing simulations of more realistic equations. These schemes will enable us to perform highfidelity simulations of turbulent flows at extreme scales with good scalability. [Preview Abstract] 
Tuesday, November 25, 2014 1:31PM  1:44PM 
R31.00003: An unconditionally stable NavierStokes solver on Octrees Maxime Theillard We present a numerical method for solving the incompressible NavierStokes equations on nongraded quadtree and octree meshes and arbitrary geometries. The viscosity is treated implicitly through a finite volume approach based on Voronoi partitions, while the convective term is discretized with a semiLagrangian scheme, thus relaxing the restrictions on the time step. A novel stable implementation of the projection step is introduced, making use of the Marker And Cell layout for the data. The solver is validated numerically in two and three spatial dimensions and challenging numerical examles are presented to illustrate its capabilities. [Preview Abstract] 
Tuesday, November 25, 2014 1:44PM  1:57PM 
R31.00004: An adaptive multiresolution gradientaugmented level set method for advection problems Kai Schneider, Dmitry Kolomenskiy, JeanChtristophe Nave Advection problems are encountered in many applications, such as transport of passive scalars modeling pollution or mixing in chemical engineering. In some problems, the solution develops smallscale features localized in a part of the computational domain. If the location of these features changes in time, the efficiency of the numerical method can be significantly improved by adapting the partition dynamically to the solution. We present a spacetime adaptive scheme for solving advection equations in two space dimensions [1]. The third order accurate gradientaugmented level set method using a semiLagrangian formulation with backward time integration is coupled with a point value multiresolution analysis using Hermite interpolation. Thus locally refined dyadic spatial grids are introduced which are efficiently implemented with dynamic quadtree data structures. For adaptive time integration, an embedded RungeKutta method is employed. The precision of the new fully adaptive method is analysed and speed up of CPU time and memory compression with respect to the uniform grid discretization are reported. \\[4pt] [1] D. Kolomenskiy, J.C. Nave and K. Schneider, arXiv:1401.7294, 2014 [Preview Abstract] 
Tuesday, November 25, 2014 1:57PM  2:10PM 
R31.00005: Stable interface treatment in overset grid methods Nek Sharan, Carlos Pantano, Daniel Bodony Overset grid methods enable complex geometry capability while retaining highorder finite differencebased discretizations; however, no provably stable methods currently exist that are free of numerical dissipation. We have developed and will present the construction of timestable interface treatments for solving hyperbolic and parabolic problems on overset grids. The treatments are based on the simultaneous approximation term (SAT) penalty method, and we use summationbyparts (SBP) operators for the derivative approximations. Error analysis is performed to determine the order of interpolation that retains the accuracy of the spatial finite difference operator. Optimal estimates on the error bound are derived and confirmed with a convergence study of numerical simulations. The conditions for the treatment to be conservative have also been determined. Numerical examples are presented to confirm the stability and accuracy of the methods. [Preview Abstract] 
Tuesday, November 25, 2014 2:10PM  2:23PM 
R31.00006: A second order accurate jump condition capturing scheme for sharp interfaces on Cartesian Grids Zhipeng Qin, Amir Riaz, Elias Balaras A robust second order accurate method is presented to solve the Possion's equation with discontinuous coefficients on uniform Cartesian grid. Volume fraction weighted average of discontinuous variables is used to implement the jump conditions. This method preserves the jump in the function and its derivatives across the interface by adding correction terms to enforce second order formal accuracy. The new method is implemented using a standard finite different discretization on a Cartesian grid leading to a robust implementation in three spatial dimensions. The coefficient matrix of the linear system is symmetric. The new method is useful for obtaining accurate pressure solutions for twophase incompressible flow. [Preview Abstract] 
Tuesday, November 25, 2014 2:23PM  2:36PM 
R31.00007: A second order accurate boundary condition capture method in irregular domain Zhipeng Qin, Amir Riaz A robust second order accurate method is presented to solve the variable coefficient Poisson's equation. One kind of volume fraction weight is used to separate different phases. This second order boundary condition capture method preserves the jumps of the function and its direction across the interface by a defined correction term. Similar to Ghost Fluid Method, the new method is implemented using a standard finite different discretization on a Cartesian grid. Therefore, it could be extended to three spatial dimensions for the case of moving interface more easily than existing methods. Furthermore, the coefficient matrix of the linear system is symmetric for the variable coefficient Poisson's equation. It is expected to be applied for NavierStoke's equation solver, ie, without the need of additional sources. [Preview Abstract] 
Tuesday, November 25, 2014 2:36PM  2:49PM 
R31.00008: Extending the fluid projection method to simulate quasistatic elastoplastic solids Chris Rycroft A wellestablished numerical approach to solve the NavierStokes equations for incompressible fluids is Chorin's projection method, whereby the fluid velocity is explicitly updated, and then an elliptic problem for the pressure is solved, which is used to project the velocity field to maintain the incompressibility constraint. In this talk, a mathematical correspondence between Newtonian fluids in the incompressible limit and elastoplastic solids in the slow, quasistatic limit will be presented. This correspondence will be used to develop a new fixedgrid, Eulerian numerical method for simulating quasistatic elastoplastic solids, whereby the stress is explicitly updated, and then an elliptic problem for the velocity is solved, which is used to project the stress to maintain the quasistaticity constraint. A number of correspondences between incompressible fluid mechanics and quasistatic elastoplasticity will be shown, creating possibilities for translating other numerical methods between the two classes of physical problems. [Preview Abstract] 
Tuesday, November 25, 2014 2:49PM  3:02PM 
R31.00009: TwoPhase Open/Outflow Boundary Conditions Suchuan Dong Twophase outflows refer to twophase flow situations where the interface between two immiscible incompressible fluids passes through open portions of the domain boundary. They are widely encountered in twophase problems involving physically unbounded domains or inflow/outflow boundaries. We present an effective outflow boundary condition, and an associated numerical algorithm, within the phase field framework for dealing with twophase outflows or open boundaries. The set of twophase outflow boundary conditions are devised to ensure the energy stability of the twophase system. They are therefore effective even in situations where strong backflows or vortices are present at the twophase outflow boundaries. Numerical simulations involving twophase inflows/outflows are discussed to demonstrate the effectiveness of the present method when large density ratios and large viscosity ratios are involved and when strong backflows are present at the twophase outflow boundaries. The method can potentially enable new investigations into the longtime behaviors and statistical features of twophase systems involving outflow/inflow boundaries. [Preview Abstract] 
Tuesday, November 25, 2014 3:02PM  3:15PM 
R31.00010: High Order SemiLagrangian Advection Scheme Carlos Malaga, Francisco Mandujano, Julian Becerra In most fluid phenomena, advection plays an important roll. A numerical scheme capable of making quantitative predictions and simulations must compute correctly the advection terms appearing in the equations governing fluid flow. Here we present a high order forward semiLagrangian numerical scheme specifically tailored to compute material derivatives. The scheme relies on the geometrical interpretation of material derivatives to compute the time evolution of fields on grids that deform with the material fluid domain, an interpolating procedure of arbitrary order that preserves the moments of the interpolated distributions, and a nonlinear mapping strategy to perform interpolations between undeformed and deformed grids. Additionally, a discontinuity criterion was implemented to deal with discontinuous fields and shocks. Tests of pure advection, shock formation and nonlinear phenomena are presented to show performance and convergence of the scheme. The high computational cost is considerably reduced when implemented on massively parallel architectures found in graphic cards. [Preview Abstract] 

R31.00011: ABSTRACT WITHDRAWN 
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