Bulletin of the American Physical Society
75th Annual Meeting of the Division of Fluid Dynamics
Volume 67, Number 19
Sunday–Tuesday, November 20–22, 2022; Indiana Convention Center, Indianapolis, Indiana.
Session G26: CFD: Shock Capturing, Discontinuous Galerkin, Higher-Order Schemes |
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Chair: Khosro Shahbazi, South Dakota Mines Room: 234 |
Sunday, November 20, 2022 3:00PM - 3:13PM |
G26.00001: A Positivity Preserving High-Order Finite Difference Method for Compressible Two-Fluid Flows Khosro Shahbazi, Daniel Boe Hyperbolicity, or the retention of a real-valued sound speed, is a required component |
Sunday, November 20, 2022 3:13PM - 3:26PM |
G26.00002: A Discontinuous Galerkin Method for Compressible Gas/Liquid Interfacial Flows William J White, Eric Johnsen Simulating compressible gas/liquid interfacial flows efficiently and with high accuracy is a challenging multi-physics problem due to large gradients, variable material properties, and disparate time and length scales. To address these challenges, we develop a discontinuous Galerkin method to solve the compressible Navier-Stokes equations using the five-equations multiphase model. The temporal scheme is explicit (Runge-Kutta) and the spatial scheme relies on a discontinuity sensor to identify regions where high-order limiting is applied, i.e., at interfaces and shock waves. The solution limiting is performed so as to prevent the generation of spurious oscillations at material interfaces by appropriately reconstructing the density, velocity, and pressure in a conservative fashion. Viscous effects and heat transfer are included and different kinds of meshes can be implemented while still maintaining arbitrarily high orders of accuracy. We demonstrate the viability of our method through a variety of one- and multi-dimensional compressible gas/liquid interfacial problems, including high-speed impact of a liquid droplet onto a rigid wall. |
Sunday, November 20, 2022 3:26PM - 3:39PM |
G26.00003: On the quantification of overshooting shock-capturing oscillations Fan Zhang An evaluation method for the shock-capturing over-amplification error (overshoot) is provided to quantitatively characterize the shock-capturing performance of nonlinear finite-difference schemes. In this evaluation method, the linear advection equation is taken as the model equation. We account for the concurrent presence of discontinuities and smooth waves, each with a complete set of supported modes. The quantitative error evaluation relies on analyzing overshoots yielded by shock-capturing schemes while solving the linear advection equation. TVD schemes and the ENO3 scheme are shown to be able to provide overshoot-free solutions, but certain schemes such as high-order WENO schemes can overshoot the exact solutions significantly in the vicinity of the discontinuities. More importantly, we can specifically and quantitatively find out the ranges of wavenumbers in which the numerical schemes are especially prone to produce overshoots. Although it is known that higher-order schemes are easier to produce overshoots, the present method quantifies the performance of shock-capturing schemes. Moreover, the present method is simple to use. |
Sunday, November 20, 2022 3:39PM - 3:52PM |
G26.00004: Primary Breakup of Liquid Jet in Supersonic Crossflows Modeled Using A Mass-Conserving Level Set Scheme Abdullahalmut Sharfuddin, Foluso Ladeinde A good number of studies has been conducted to model breakup of liquid jet by subsonic airflows. However, itssupersonic equivalent has not received enough attention due to computational complexities involved. In this work, we formulate a mass-conserving level set scheme that is suitable for high-speed applications. Since the interface between the supersonic gas flow and the subsonic liquid flow is marked by a high-density ratio (of a thousand or more), the instabilities occurring at the interface need to be resolved with high accuracy. In our study, the gaseous region is compressible while the liquid region is assumed incompressible. The compressible domain has been resolved using a MUSCL based high resolution scheme that has a shock capturing ability. The incompressible domain is calculated with a pressure correction scheme to reduce computational costs. The level set method has been coupled with the volume of fluid method through a functional relationship between the level set and the volume of fluid functions. In this manner, mass is conserved while a sharp description of the interface is maintained. We present our results first in two dimensions and verify them by comparing with other numerical studies. Then we extend our model to three dimensions and validate our results against experimental findings. |
Sunday, November 20, 2022 3:52PM - 4:05PM |
G26.00005: Popping the cork of champagne bottle: simulating the coupled gas and cork dynamics Lukas Wagner, Stefan Braun, Bernhard F Scheichl We present a numerical study of the gas jet formed by the release of carbon dioxide at the sudden opening of a champagne bottle, typically sealed with a cork stopper, and its mixing with the exterior air. This investigation is stimulated by (and complements) the seminal experimental investigation carried out by Liger-Belair, Cordier & Georges (Science Advances, 5(9), 2019). Before the opening, the gas is at rest as confined by the stopper and the liquid, taken as quiescent throughout and having a constant level of a plane free surface. The whole flow configuration is assumed to be axisymmetric, and the contained gas and the air are taken as indistinguishable and thus perfectly mixable ideal gases. The resulting problem is governed by the Euler equations, governing the inviscid gas flow as suitably expressed in conservative form, the equation of motion of the stopper, and the kinematic and dynamic boundary conditions met on the bottle walls and the stopper surface. There they account for the propagation of the cork by the pressure forces exerted by the flow and, as long as the stopper has not completely left the bottleneck, the normal and Coulomb friction forces due to its sliding along the latter. The compressibility of the cork is considered through its typical hyperelastic constitutive behavior. We employed the open-source gas dynamics simulation package Clawpack to solve the so obtained fluid-structure interaction problem. Some modifications of the underlying Godunov's and Roe's schemes proved necessary so as to resolve the fast axial motion of the cork with due accuracy. As a definite highlight, in good agreement with the experimental findings, our results disclose the formation of Mach disk between the bottle opening and the freely moving cork as well as a precursor shock in front of it. We discuss the dependence of the solutions on the temperature of the contained gas and their potential impact on problems in the wider context of transitional ballistics. |
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