Bulletin of the American Physical Society
72nd Annual Meeting of the APS Division of Fluid Dynamics
Volume 64, Number 13
Saturday–Tuesday, November 23–26, 2019; Seattle, Washington
Session C19: CFD: Highorder and Shockcapturing Methods 
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Chair: Bryce Campbell, Lawrence Livermore National Laboratory Room: 401 
Sunday, November 24, 2019 8:00AM  8:13AM 
C19.00001: Highorder energystable boundary treatment for finitedifference cutcell method Nek Sharan, Peter Brady, Daniel Livescu Cutcell methods simplify grid generation for fluidflow simulations over complex geometries. Construction of highorder boundary implementation for cutcell discretization that also provably satisfies stability and conservation constraints, however, remains a challenge, especially for hyperbolic equations. Existing energystability proofs of finitedifference methods for initialboundary value problems require imposing the boundary conditions weakly or by a projection approach, where the computed boundary values may not be exact. Inexact boundary values may be adequate for estimates in certain applications, but they can adversely influence turbulence/mixing statistics in a direct numerical simulation. A framework to prove energystability with strong boundary treatment is developed and used to obtain boundary implementation for a Cartesian cutcell discretization. Linear and nonlinear numerical tests to verify the accuracy, stability and conservation properties of the developed method will be discussed. [Preview Abstract] 

C19.00002: ABSTRACT WITHDRAWN 
Sunday, November 24, 2019 8:26AM  8:39AM 
C19.00003: Multidimensional optimization of nonlinear shock capturing schemes Raynold Tan Yiyun, Andrew Ooi, Richard Sandberg In this work, a quasilinear semidiscrete analysis of shock capturing schemes in multidimensional wavenumber space is proposed. Using the dispersion relation of the two dimensional convection and linearized Euler equations, the spectral properties of a spatial scheme can be quantified in two dimensional wavenumber space. A hybrid scheme which combines the merits of the Minimum Dispersion and Controllable Dissipation (MDCD) scheme with the Targeted Essentially NonOscillatory (TENO) scheme was developed. Using the proposed analysis framework, the hybrid scheme was spectrally optimized in multidimensional wavenumber space such that the linear part of the scheme can be separately optimized for its dispersion and dissipation properties. In order to demonstrate the improved spectral properties of the new scheme, a series of one dimensional and multidimensional numerical tests were conducted. [Preview Abstract] 
Sunday, November 24, 2019 8:39AM  8:52AM 
C19.00004: An arbitrarily highorder, conservative, Cartesiangrid interface tracking scheme for multiphase flow simulations Bryce Campbell This work describes a newly developed conservative, highorder, Cartesiangrid method for tracking the interface in a multiphase flow. An efficient reconstruction scheme is proposed that utilizes the volume fraction field to generate a bspline approximation for the interface. This interface representation is globally conservative, and analytical differentiation of the spline allows for the interfacial normal vectors and curvatures to be obtained directly. A separate algorithm is proposed that conservatively advects the interface due to an arbitrary (compressible/incompressible) velocity field. These reconstruction and advection methods have been successfully tested against the standard benchmark problems such as the: advection of a circle in uniform or corner flows, vortexinabox, and collapsing/imploding circle tests. Together, the proposed reconstruction and advection techniques can achieve arbitrarily high (user specified) mesh convergence rates and conserve to within machine precision accuracy. The twodimensional formulation may be easily extended to the more general threedimensional problem. [Preview Abstract] 
Sunday, November 24, 2019 8:52AM  9:05AM 
C19.00005: Highorder simulation of flow around geometries on octree meshes using Brinkmann penalization. Sabine Roller, Harald Klimach, Nikhil Anand, Neda Ebrahimi Pour Simulation of flow and acoustics over large domains and long distances require highly efficient CFD methods as well as highly scalable implementations on modern supercomputers. Highorder Discontinous Galerkin (DG) implemented on octree meshes fulfill these requirements. Unfortunately, the representation of obstacles in the domain  which usually cause the generation of acoustics  is an issue for highorder methods. In combination with the high order DG (orders up to 32 or 64, i.e. \textgreater \textgreater 2) the representation of the obstacle surface needs to hold an approximation order equivalent to the scheme order, otherwise the scheme looses its best property at exactly that point. This contribution will investigate the implementation of geometry representations with highorder on a given Cartesian mesh by using a Brinkmann penalization strategy. \newline [1] Roller S. et al. (2011): An Adaptable Simulation Framework Based on a Linearized Octree. In: Resch M., Wang X., Bez W., Focht E., Kobayashi H., Roller S. (eds) High Performance Computing on Vector Systems 2011. Springer, Berlin, Heidelberg\newline [2] Q. Liu, O.V. Vasilyev, A Brinkmann method for compressible flows in complex geometries, In Journal of Computational Physics 227, Elsevier Inc. 2007 [Preview Abstract] 
Sunday, November 24, 2019 9:05AM  9:18AM 
C19.00006: A numerical strategy for efficient multiscale and multiphysics simulations using partitioned coupling Neda Ebrahimi Pour, Sabine Roller The simulation of complex problems such as multiscale and multiphysics is still challenging when considering the computational efficiency of those simulations. Simulating all these effects in a single domain is not feasible monolithically, since different scales appear in different areas of the domain, which have to be resolved properly. In order to simulate these kinds of problems in a more efficient way, we make use of partitioned coupling, where we split the domain into subdomains where each of them uses the appropriate set of equations, scheme order and mesh resolution. The subdomains are weakly connected to each other at the boundaries. For the communication and dataexchange between them a coupling approach integrated in our simulation framework APES is used. We will present first results of the coupled scenario and show how well we can reduce the computational cost, when compared to the monolith simulation by means of a small test case, which is still feasible monolithically. [Preview Abstract] 
Sunday, November 24, 2019 9:18AM  9:31AM 
C19.00007: A secondorder method for convectiondiffusion equation across interfaces separated by boundaries of flow Xianglong Wang, Mark Meyerhoff, Joseph Bull Biological mass transport often involves transport across interfaces separated by presence of flow. An example is the recent development of nitric oxide releasing catheters that release nitric oxide into the bloodstream to prevent biofilm formation. The presence of flow often creates large gradients in mass concentration with sharp contrast in Peclet numbers across the interface. Solving such problems with computational methods are challenging, since proper shock capturing methods are essential to resolve these shocks. Our goal is to accurately resolve the shocks present in convectiondiffusion problems separated by boundaries of flow. To achieve this goal, we developed a 3D Cartesiancoordinates based method on a model problem simulating release of substancedoped catheters into the bloodstream on a nonorthogonal hexagonal grid. We applied proper directional slope limiting for calculating convection flux and multipoint flux approximation (MPFA) Lmethod for calculating diffusion flux. This method allows us to achieve stable solutions of the convectiondiffusion equation in our model problem with near secondorder accuracy for local Peclet numbers up to 5.0. The ability of perform such simulation is essential for guiding the development of nitric oxide releasing catheters. [Preview Abstract] 
Sunday, November 24, 2019 9:31AM  9:44AM 
C19.00008: Datadriven optimization strategies for staggeredgrid Lagrangian methods Jason Albright, Mikhail Shashkov, Nathan Urban For applications dealing with shock waves, algorithmic ingredients like artificial viscosity are essential to avoid highly oscillatory solutions. Yet they also introduce additional model parameters that are usually poorly constrained and consequently are often handtuned to problem specific applications. In this talk, we produce optimal values for parameters controlling the amount of artificial viscosity and artificial heat flux through a combination of large ensemble sampling and machine learningbased optimization techniques. We illustrate that the optimal parameter set significantly improves the accuracy, efficiency, and flexibility of the underlying scheme. Although, we illustrate this strategy for a particular discretization scheme, this methodology may be generalized to a much wider variety of existing methods. [Preview Abstract] 
Sunday, November 24, 2019 9:44AM  9:57AM 
C19.00009: Reconstructing the piecewisesmooth solution of the Poisson equation for Chebyshevcollocation solution with pointwise exponential convergence Sudipta Ray, Sandeep Saha Computation of an exponentially accurate solution of the Poisson equation which is discontinuous across an interface is restricted by the occurrence of the \emph{Gibbs phenomenon}. Spectral discretization with inaccurate implementation of the jump conditions produces aphysical oscillations in the numerical solution with algebraic convergence. In the present work, a Chebyshevcollocation spectral discretization is implemented to compute the piecewisesmooth solution of the Laplace and the Poisson equation in two dimensions, where the solution domain contains an interface of complex geometrical shape. The solution is expressed as the sum of a smooth function and a modified Heaviside function at the interface. The unit Heaviside step function is weighted by a smooth jump function which allows the conditions at the interface to be imposed exactly. The modified Heaviside function for interface conditions on the solution and the gradient along the normal is expressed with a weak form expansion. In the presence of global information on the jumps in the form of analytical expressions, the method demonstrates pointwise exponential convergence for the problems considered. In addition, the method appears to be insensitive to perturbations to the interface below the local grid spacing. [Preview Abstract] 
Sunday, November 24, 2019 9:57AM  10:10AM 
C19.00010: Reconstructing the piecewisesmooth solution of ordinary differential equations for Chebyshevcollocation solution with pointwise exponential convergence Sandeep Saha, Sudipta Ray Physical problems with interfacial discontinuity in the solution or material property are characterized by piecewisesmooth solutions. Numerical computation of problems with interfacial discontinuity requires accurate resolution of the interface conditions. For finiteorder methods, the problem may be resolved with local corrections near the interface. Application of spectral methods to approximate the piecewisesmooth solution without an accurate implementation of interface conditions, however, results in the \emph{Gibbs oscillations} and nonconvergent numerical solution. In order to overcome the \emph{Gibbs phenomenon}, the discontinuous solution is expressed as the sum of a smooth function and a modified Heaviside function at the location of the discontinuity. The unit Heaviside step function is modified with a smooth jump function which exactly satisfies the conditions of discontinuity at the interface. A weak form expansion of the jump function that uses interface conditions upto the first derivative for a secondorder ordinary differential equation is proposed. Implementation of a Chebyshevcollocation discretization to problems where the discontinuities in the solution are known in analytic form produces numerical solution that converges exponentially in the maximum norm. [Preview Abstract] 
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