We propose a unified interpolation stencil that is used for a ghost-cell immersed boundary method to satisfy wall boundary conditions in Cartesian-based numerical simulation of fluid flow with complex boundaries. As other ghost-cell methods do, the numerical boundary point is considered in the solid region and the required velocity is interpolated directly from the proximate points in the fluid region. In this paper, we propose a unified interpolation scheme based on a sequence of one-dimensional interpolations. Different interpolation stencils are examined and their convergence rates are compared by solving a benchmark problem on the flow between the concentric cylinders. In contrast to typical standard stencils, the proposed ones are versatile and do not require to be altered according to the irregularities in boundary shape. Namely, the boundary condition can be accurately imposed with a unique stencil for all numerical boundary points while preserving the convergence rate of the flow solver. Performance of the proposed method is studied by solving two-dimensional incompressible flows around a circular cylinder, a square cylinder, and a square cylinder inclined with respect to the main flow. Comparison with the existing numerical and experimental data shows good agreement, which confirms the capability of the proposed method.
As an extension of the immersed boundary method with unified interpolation stencil (Kor, Badri Ghomizad, and Fukagata, J. Fluid Sci. Technol., Vol. 12, 2017, JFST0011), we propose an immersed boundary method that can handle moving boundary problems with a lower level of spurious force oscillation. The key modification to the previously proposed method, which was validated for fixed boundary problems, is to adopt the reconstruction method, in which the velocities outside the body are reconstructed, instead of the ghost-cell method, in which the velocities inside the body are set to satisfy the boundary conditions. From the comparison between the ghost-cell and reconstruction methods, both methods work equally well for a fixed boundary problem, but the reconstruction method is found to be effective in suppressing the spurious force oscillations that appear in moving boundary problems. The capability of the proposed method is demonstrated by numerical investigations of some typical problems. Both predefined motions, such an oscillating cylinder and a hovering flat plate, and interacting motions of rigid bodies are simulated to validate the method. For the latter, sedimentation of a single cylinder as well as a group of interacting cylinders under the gravitational force is examined to demonstrate the capability of the present method for fluid-structure interaction problems. The results show that the proposed method can properly handle the moving boundary problems, while preserving the simplicity of the unified interpolation stencil.
We develop a versatile and accurate structured adaptive mesh refinement (S-AMR) strategy with a moving least square sharp-direct forcing immersed boundary method (IBM) for incompressible fluid-structure interaction (FSI) simulations. The computational grid consists of several nested blocks in different refinement levels. While blocks with the coarsest grid cover the entire computational domain, the computational domain is locally refined at the location of solid boundary (moving or fixed) by bisecting selected blocks in every coordinate direction. The grid topology and data structure is managed by an extended version of Afivo toolkit (Teunissen and Ebert, 2018), where a novel technique is introduced for conservative data transfer between the coarser and the finer blocks, particularly in velocity transformation for which the mass conservation plays a crucial role. In the present study, the continuity and Navier-Stokes equations for incompressible flows are spatially discretized with a second order central finite difference method using a collocated arrangement and are time-integrated using a semi-implicit second order fractional step method, although the proposed S-AMR strategy can be used with different discretization schemes. An IBM using a moving least square approach is utilized to impose boundary conditions. To handle FSI problems, all the governing equations for the dynamics of fluid and structure are simultaneously advanced in time by a predictorcorrector strategy. Several test cases of increasing complexity are solved in order to demonstrate the robustness and accuracy of the proposed method as well as its capability in simulation-driven mesh adaptivity.
Based on the Moving Least Square (MLS) approximation, we propose a sharp interface direct-forcing immersed boundary method for incompressible fluid flows with fixed and moving boundaries. Since the domain of definition for the interpolation is highly flexible and the MLS approximation provides an accurate reconstructed approximation of the solution, the proposed method serves the precision and versatility required for a numerical framework to study the fluid-structure interaction problems. To alleviate the inherent spurious numerical oscillation that occurs in the calculated forces on moving boundary embedded objects, we use a two step predictor-corrector method in which the direct forcing terms are calculated after the predictor step and imposed on the whole solid domain as well as at the immediate vicinity of the solid boundary inside the fluid domain. To represent the arbitrary geometries, we adopt a signed distance function representation of the rigid body and an interpolation strategy to considerably reduce the computational cost of the re-initialization of the distance function at every time step. The potential capability of the method is demonstrated for both fixed and moving boundary problems. We also solve a sedimentation of a single cylinder to demonstrate the ability of the present method in solving fluid-structure interaction problems. These numerical experiments show that the proposed moving least square immersed boundary method can handle relatively complex moving problems while enjoying a versatile interpolation strategy and keeping the boundary conditions sharp with remarkable accuracy.
The present paper, based on the vorticity-velocity formulation of the Navier-Stokes equations, proposes an immersed boundary method for the simulation of heat transfer problems within a geometrically complex domain. The desired boundary conditions are imposed by the direct modification of the initial conditions of vorticity transport and energy equations using smooth interpolations. The time advancement of both transport equations is performed by the explicit fourth-order Runge-Kutta method. One of the main objectives of this paper is to present global smooth interpolations to evaluate the local Nusselt number. The forced convection of moving and fixed circular cylinders, natural convection problem in complex geometries, and the mixed convection between two concentric cylinders-at various Reynolds numbers-are studied. ARTICLE HISTORY
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