2018/12/30 by Bahman Aboulhasanzadeh, Aboulhasanzadeh, Bahman, Kamran Mohseni +1
Engineering · Mathematics · Physics and Astronomy · #Advanced Numerical Methods in Computational Mathematics #Algorithm #Applied mathematics #Classical mechanics #Compressibility #Compressible flow #Computation #Computational Fluid Dynamics and Aerodynamics #Computational Physics (physics.comp-ph) #Computer science #Euler equations #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Fluid Dynamics and Turbulent Flows #Gas Dynamics and Kinetic Theory #Inviscid flow #Mathematical analysis #Mathematics #Mechanics #Observability #Observable #Physics #Regularization (linguistics) #physics.comp-ph #physics.flu-dyn
paper · pdf · doi:10.48550/arxiv.1812.11569
published in arXiv (Cornell University) (Cornell University)
arxiv created 2018/12/30 · openalex publication_date 2018/12/30 · arxiv updated 2019/01/01 · openalex created_date 2022/10/01 · openalex updated_date 2026/08/05
Most fluid flow problems that are vital in engineering applications involve\nat least one of the following features: turbulence, shocks, and/or material\ninterfaces. While seemingly different phenomena, these flows all share\ncontinuous generation of high wavenumber modes, which we term the 'k_\∞\nirregularity.' In this work, an inviscid regularization technique called\n'observable regularization' is proposed for the simulation of two-phase\ncompressible flows. The proposed approach regularizes the equations at the\nlevel of the partial differential equation and as a result, any numerical\nmethod can be used to solve the system of equations. The regularization is\naccomplished by introducing an 'observability limit' that represents the length\nscale below which one cannot properly model or continue to resolve flow\nstructures. An observable volume fraction equation is derived for capturing the\nmaterial interface, which satisfies the pressure equilibrium at the interface.\nThe efficacy of the observable regularization method is demonstrated using\nseveral test cases, including a one-dimensional material interface tracking,\none-dimensional shock-tube and shock-bubble problems, and two-dimensional\nsimulations of a shock interacting with a cylindrical bubble. The results show\nfavorable agreement, both qualitatively and quantitatively, with available\nexact solutions or numerical and experimental data from the literature. The\ncomputational saving by using the current method is estimated to be about one\norder of magnitude in two-dimensional computations and significantly higher in\nthree-dimensional computations. Lastly, the effect of the observability limit\nand best practices to choose its value are discussed.\n