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

JOURNAL OF COMPUTATIONAL PHYSICS

卷:390

Article

Sakurai, Teluo¹  Yoshimatsu, Katsunori²  Okamoto, Naoya^3,6  Schneider, Kai^4,5 

[1] Nagoya Univ, Dept Computat Sci & Engn, Nagoya, Aichi 4648603, Japan

[2] Nagoya Univ, Inst Mat & Syst Sustainabil, Nagoya, Aichi 4648601, Japan

[3] Nagoya Univ, Ctr Computat Sci, Nagoya, Aichi 4648603, Japan

[4] Aix Marseille Univ, I2M, CNRS, 39 Rue F Joliot Curie, F-13453 Marseille 13, France

[5] Cent Marseille, 39 Rue F Joliot Curie, F-13453 Marseille 13, France

[6] Aichi Inst Technol, 1247 Yachikusa,Yakusacho, Toyota 4700392, Japan

关键词: Volume penalization;    Inhomogeneous Neumann boundary conditions;    Poisson equation;    Scalar flux;   

DOI  :  10.1016/j.jcp.2019.04.008

来源: Elsevier

【 摘 要 】

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. (2012) [4]. 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. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free