Bulletin of the American Physical Society
66th Annual Meeting of the APS Division of Fluid Dynamics
Volume 58, Number 18
Sunday–Tuesday, November 24–26, 2013; Pittsburgh, Pennsylvania
Session R5: CFD VIII: Numerical Methods II |
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Chair: Oleg V. Vasilyev, University of Colorado Room: 327 |
Tuesday, November 26, 2013 1:05PM - 1:18PM |
R5.00001: High-order discontinuous-Galerkin simulations of flows over airfoils with curved boundaries Daniel Nelson, Gustaaf Jacobs We compare the flow around a NACA 65-(1)412 airfoil using straight sided and curved sided boundary subdomains in a discontinuous-Galerkin spectral element computation. Specifically, we examine the structure of the vortex street wake and note significant differences in the wake dynamics between the two boundary subdomain implementations. At a Reynolds number of 20,000, the boundary layer on the suction side of the airfoil separates at approximately 60\% of the cord length behind the leading edge. The resulting unstable shear layer interacts with vortices generated at the trailing edge to form a vortex street wake. When the subdomain boundary is fitted to the airfoil spline with a curved side, the location of the separation point is fixed and the vortex street is regular and periodic. When straight-sided subdomains are used, the separation point alternates erratically between subdomain corners, resulting in an aperiodic roll-up of the shear layer and subsequent aperiodicity in the near and far wake. [Preview Abstract] |
Tuesday, November 26, 2013 1:18PM - 1:31PM |
R5.00002: Extended Discontinuous Galerkin Methods for tow-phase flows Florian Kummer Multiphase flows of two (or more) immiscible fluids occur in multiple technical relevant application, e.g. pre-mixed combustion, evaporation or sprays. Since density and viscosity are discontinuous at the interface between the two fluids, the pressure and velocity field contain singularities. For material interfaces, the presence of surface tension will induce a jump in the pressure field. Solutions for non-material interfaces contain jumps in velocity and pressure field, even without any surface tension models. The numerical treatment of these jumps, and the high gradients which are induced by them, is challenging. This is especially true for high-order methods, like the discontinuous Galerkin (DG) method, that usually show their major advantage--the high convergence order--only for smooth solutions. We will present an Extended Discontinuous Galerkin (XDG) method that is able to represent jumps mentioned above with sub-cell accuracy. The interface between the two fluids is represented by a high-order DG-based level set method. In cells which are cut by the interface, separate degrees-of-freedom are employed for both faces. At the interface, the jump conditions are discretized in a weak sense, in order to couple both phases. [Preview Abstract] |
Tuesday, November 26, 2013 1:31PM - 1:44PM |
R5.00003: Eliminating resonances in the Galerkin-truncated Burgers and Euler equations using wavelet filtering Kai Schneider, Rodrigo Pereira, Romain Nguyen van yen, Marie Farge It is well known that solutions to the Fourier-Galerkin truncation of the inviscid Burgers equation (and other hyperbolic conservation laws) do not converge to the physically relevant entropy solution after the formation of the first shock. This loss of convergence was recently studied in detail in [S.S. Ray et al., Phys. Rev. E 84, 016301 (2011)], and traced back to the appearance of a spatially localized resonance phenomenon perturbing the solution. In this work, we propose a way to cure this resonance by filtering a wavelet representation of the Galerkin-truncated equations. A method previously developed with a complex-valued wavelet frame is applied and expanded to embrace the use of real-valued orthogonal wavelet basis, which we show to yield satisfactory results only under the condition of adding a safety zone in wavelet space. We also apply the complex-valued wavelet based method to the 2D Euler equation problem, showing that it is able to filter the resonances in this case as well. For details we refer to R. Pereira et al., Phys. Rev. E 87, 033017, 2013. [Preview Abstract] |
Tuesday, November 26, 2013 1:44PM - 1:57PM |
R5.00004: Model Order Reduction for the Coupled System of Flow and Moving Structure Haotian Gao, Mingjun Wei Traditional POD-Galerkin projection, as a popular approach for model reduction, is applied in a fixed fluid domain which, however, is not the case for many fluid-solid systems with moving objects/boundaries. Instead of treating a time-dependent fluid domain, we consider the combination of fluid and solid one single stationary domain. The idea, which is similar to immersed boundary technique used in numerical simulation, is having original Navier-Stokes equation in the combined and fixed fluid-solid domain and adding extra body-force terms to the equation only in solid area to represent the moving boundary or solid structure. Global POD modes can then be achieved with a special inner product also defined in the combined domain. With both the modes and equations defined in a fixed fluid-solid domain, the Galerkin projection is applied directly in the same domain and provides a global reduced-order model for the system. In comparison to the traditional approach, the new global model ends up with extra terms to represent solid motion and our preliminary results have shown that these terms are critical in sustaining system energy. [Preview Abstract] |
Tuesday, November 26, 2013 1:57PM - 2:10PM |
R5.00005: A Robust Integration Method for Stiff Transport Equations Jose Escobar, Ismail Celik Numerical simulation of reactive flows is one of the most difficult problems in Computational Fluid Dynamics (CFD). The difficulties are mainly due to the wide range of characteristic time scales present in the mass production/consumption sources which lead to a stiff system of governing equations. Classical integration methods such as explicit Euler method are restricted by the smallest characteristic time scale, and the explicit Runge-Kutta (RK) methods require intermediate predictor-corrector steps which make the problem computationally expensive. Implicit methods are also computationally expensive due the calculation of the Jacobian which makes their implementation difficult for reactive systems with tens of chemical species and hundreds of reactions. The current study explores the possibility of solving the transport equations for species concentrations faster than the standard methods without compromising accuracy. The present approach is based on transformation of the variable of interest using the hyperbolic tangent function. The proposed transformation also has the advantage of ensuring that the value of the variable of interest to be always in the range from zero to one, which is highly desirable when solving for specie mass or molar fractions. The possibility of using much larger time steps compared to the classical methods is an additional advantage. [Preview Abstract] |
Tuesday, November 26, 2013 2:10PM - 2:23PM |
R5.00006: Level Set Jet Schemes for Stiff Advection Equations David Salac, Ebrahim Kolahdouz The stable and accurate modeling of stiff multiphase fluid systems represent a major challenge. In this talk strategies to employ the Jet Level Set scheme of Nave et. al. in stiff advection problems, such as lipid bilayer vesicle simulations, are presented. The rational and sample implementations of these methods will be shown. The results will demonstrate that the strict time-step restrictions can be alleviated without greatly reducing the accuracy of the method. [Preview Abstract] |
Tuesday, November 26, 2013 2:23PM - 2:36PM |
R5.00007: An Improved Advection Scheme for Implicit Interfaces on Cartesian Grids Zhipeng Qin, Amir Riaz, Elias Balaras, Keegan Delaney A new approach is presented to reinitialize the level set function by a direct projection of interface topology. The interface topology is built with the help of 2nd order interpolation reconstruction and interface smoothing by least squares fitting scheme. With the help of three kinds of errors the new approach is shown to both conserve mass and maintain topology during advection. Existing methods for the advection of implicit interfaces, such as classical redistance techniques and interface recompression methods, are compared with the new scheme. The improvement achived by the new scheme is demonstrated on uniform Cartesian grids for 2D vortex and two-phase incompressible rising bubble cases. [Preview Abstract] |
Tuesday, November 26, 2013 2:36PM - 2:49PM |
R5.00008: An Iterative Brinkman penalization for particle vortex methods J.H. Walther, M.M. Hejlesen, A. Leonard, P. Koumoutsakos We present an iterative Brinkman penalization method for the enforcement of the no-slip boundary condition in vortex particle methods. This is achieved by implementing a penalization of the velocity field using iteration of the penalized vorticity. We show that using the conventional Brinkman penalization method can result in an insufficient enforcement of solid boundaries. The specific problems of the conventional penalization method is discussed and three examples are presented by which the method in its current form has shown to be insufficient to consistently enforce the no-slip boundary condition. These are: the impulsively started flow past a cylinder, the impulsively started flow normal to a flat plate, and the uniformly accelerated flow normal to a flat plate. The iterative penalization algorithm is shown to give significantly improved results compared to the conventional penalization method for each of the presented flow cases. [Preview Abstract] |
Tuesday, November 26, 2013 2:49PM - 3:02PM |
R5.00009: Characteristic-based Volume Penalization Method for Arbitrary Mach Flows Around Solid Obstacles Nurlybek Kasimov, Eric Brown-Dymkoski, Oleg Vasilyev A new volume penalization method to enforce boundary conditions on solid/moving/deformable obstacles of arbitrary shape for both Navier-Stokes and Euler equations is presented. The approach extends the Brinkman penalization to generalized Neumann and Robin boundary conditions by introducing hyperbolic penalization terms with characteristics pointing inward on solid obstacles. The boundary conditions for both integrated and non-integrated variables can be imposed in a systematic manner that parallels the prescription of exact boundary conditions. A principle advantage of the method is that it provides a systematic means of controlling the error. This approach is general and applicable to a wide variety of flow regimes. Examples of supersonic/subsonic viscous/inviscid complex geometry flows are given and discussed. [Preview Abstract] |
Tuesday, November 26, 2013 3:02PM - 3:15PM |
R5.00010: A conservative adaptive wavelet method for the shallow water equations on the sphere Nicholas Kevlahan, Matthias Aechtner, Thomas Dubos This talk presents the first dynamically adaptive wavelet method for the shallow water equations on a staggered hexagonal C-grid on the sphere. Pressure is located at the centres of the primal grid (hexagons) and velocity is located at the edges of the dual grid (triangles). Distinct biorthogonal second generation wavelet transforms are developed for the pressure and the velocity. These wavelet transforms are based on second-order accurate interpolation and restriction operators. Together with compatible restriction operators for the mass flux, circulation and Bernoulli function, they ensure that mass is conserved and that there is no numerical generation of vorticity when solving the shallow water equations. The shallow water equations are discretized on the dynamically adapted multiscale grid using a mass and potential-enstrophy conserving finite-difference scheme. The method is applied to a zonal jet test case, turbulence on the rotating sphere and western boundary current flow. Solid boundary conditions are implemented using a new multiscale penalization of the shallow water equations. [Preview Abstract] |
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