A characteristic based volume penalization method for general evolution problems applied to compressible viscous flows

Brown-Dymkoski, Eric; Kasimov, Nurlybek; Vasilyev, Oleg V.

doi:10.1016/j.jcp.2013.12.060

Cited by 64 publications

(74 citation statements)

References 22 publications

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“…Penalization techniques for Neumann and Robin boundary conditions are more recent and less developed, see e.g., Refs. [4][5][6][7][8][9]. Most immersed boundary methods result in low order, i.e., first or second order, approximation and computational stiffness.…”

Section: Introductionmentioning

confidence: 99%

Volume penalization for inhomogeneous Neumann boundary conditions modeling scalar flux in complicated geometry

Sakurai

Yoshimatsu

Okamoto

et al. 2019

Journal of Computational Physics

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We develop a volume penalization method for inhomogeneous Neumann boundary conditions, generalizing the flux-based volume penalization method for homogeneous Neumann boundary condition proposed by Kadoch et al. [J. Comput. Phys. 231 (2012) 4365]. The generalized method allows us to model scalar flux through walls in geometries of complex shape using simple, e.g. Cartesian, domains for solving the governing equations. We examine the properties of the method, by considering a one-dimensional Poisson equation with different Neumann boundary conditions. The penalized Laplace operator is discretized by second order central finite-differences and interpolation. The discretization and penalization errors are thus assessed for several test problems. Convergence properties of the discretized operator and the solution of the penalized equation are analyzed. The generalized method is then applied to an advection-diffusion equation coupled with the Navier-Stokes equations in an annular domain which is immersed in a square domain. The application is verified by numerical simulation of steady free convection in a concentric annulus heated through the inner cylinder surface using an extended square domain. a yoshimatsu@nagoya-u.jp

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Section: Introductionmentioning

confidence: 99%

Volume penalization for inhomogeneous Neumann boundary conditions modeling scalar flux in complicated geometry

Sakurai

Yoshimatsu

Okamoto

et al. 2019

Journal of Computational Physics

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“…However, most of these approaches are based on incompressible formulations. Recently, Brown-Dymkoski et al [34] developed a characteristic-based volume penalization method for compressible flow based on an extension of the Brinkman Penalization Method that allows any arbitrary Dirichlet, Neumann, or…”

Section: Immersed Boundary Methodsmentioning

confidence: 99%

“…The approach is to perform 2-D simulations of shock waves impacting an array or cloud of particles, where the same Mach number and particle configuration used in Regele et al [31] is used for consistency. The fully compressible Navier-Stokes equations are solved with a characteristic based volume penalization method [34], which provides a more accurate estimate of the magnitude of these terms than the previous Euler simulations [31]. A transverse array of particles is used to obtain deeper insight into the wave dynamics and unsteady vortex generation on each particle under the mutual wave-wave and wave-wake interaction between the particles.…”

Section: Introductionmentioning

confidence: 99%

Investigation and quantification of flow unsteadiness in shock-particle cloud interaction

Hosseinzadeh-Nik

Subramaniam

Regele

2018

International Journal of Multiphase Flow

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This work aims to study the interaction of a shock wave with a cloud of particles to quantify flow unsteadiness and velocity fluctuations using particle-resolved direct numerical simulation (PR-DNS). Three cases are studied, with each case revealing one aspect of the intricate flow phenomena involved in this interaction. The unsteady interaction of a shock wave with a transverse array of particles reveals the origin of unsteadiness under the effect of mutual wave-wave and wave-wake interactions between the particles. In the second case, the interaction of a shock with a particle cloud is studied, with a focus on the interaction of the complex wave system with the vortical structure. A budget analysis of the vorticity equation reveals the sources of strong unsteadiness in the particle cloud. A detailed analysis of the velocity fluctuation and kinetic energy in the fluctuating motion is performed to ascertain the importance of the velocity fluctuations that arise from the strong unsteadiness. An analogous analysis is presented, in the third case, for a gradually-induced flow on the same particle cloud along with a comparison to the shock induced case to assess the impulsive effect of shock on intensity of the fluctuating field statistics.

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“…In order to reduce computational costs, wavelet threshold filtering and traditional turbulence models are integrated to generate many useful methods, e.g., Wavelet Direct Numerical Simulation (W-DNS), Coherent Vortex Simulation (CVS), and Stochastic Coherent Adaptive Large Eddy Simulation (SCALES). However, it has been recognized that these methods would be applied in other fields, e.g., astrophysics and oceanography [10][11][12][13][14][15][16].…”

Section: Introductionmentioning

confidence: 99%

Wavelet Methods and Adaptive Grids in One-Dimensional Movable Boundary Problems

Xu¹,

Tan

Li³

2020

Mathematical Problems in Engineering

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Adaptive wavelet collocation methods use wavelet transform and filtering to generate adaptive grids. However, if the boundary moves, the grid becomes aberrant. It baffles wavelet transform and makes the adaptive wavelet methods lose advantages on computational efficiency. This paper develops a series of methods or skills to effectively perform wavelet transform and to generate adaptive grids for one-dimensional movable boundary problems. The methods remain the original inner grid points and keep the grid in the original-nested structure, in order to remain scanty during the whole computing process. For boundary extending, the adaptive wavelet program begins to run on the very new grid beyond the original boundary once it reaches a nested structure, which is called the Intermittent Adaptive Method as a consequence. If the boundary extends tremendously, the new nested grids can be combined to a greater nested grid for further efficiency, which is named the Grid Combine Method. While for boundary contracting, a fictitious boundary is addressed to replace the original boundary that will recede, so wavelet transform can be successfully performed on the original nested grid. Finally, two numerical tests, local features moving and gas gun, were resolved and discussed to show the evolution process of the adaptive grids with the boundaries moving. For boundary contracting, the valid points decrease because the computation domain recedes; while for boundary extending, the valid point numbers vary between a range that almost remains unchanged.

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A characteristic based volume penalization method for general evolution problems applied to compressible viscous flows

Cited by 64 publications

References 22 publications

Volume penalization for inhomogeneous Neumann boundary conditions modeling scalar flux in complicated geometry

Volume penalization for inhomogeneous Neumann boundary conditions modeling scalar flux in complicated geometry

Investigation and quantification of flow unsteadiness in shock-particle cloud interaction

Wavelet Methods and Adaptive Grids in One-Dimensional Movable Boundary Problems

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