Second-order Interpolation Techniques for Accurate Surface Data Estimation in Immersed-Boundary Methods
25 Jun 2018-
About: The article was published on 2018-06-25. It has received 1 citations till now. The article focuses on the topics: Interpolation & Boundary (topology).
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01 Jan 2020
TL;DR: In this paper, a sharp-interface immersed boundary method for compressible, turbulent flows and its application to transonic/supersonic flows is discussed, where the flow properties in the immediate neighbourhood of the immersed surface are reconstructed using inverse distance-based interpolation procedures.
Abstract: In this chapter, we discuss the development of a sharp-interface immersed boundary method for compressible, turbulent flows and its application to transonic/supersonic flows. A direct-forcing-type immersed boundary method is elucidated wherein the flow properties in the immediate neighbourhood of the immersed surface are reconstructed using inverse distance-based interpolation procedures. The flow is assumed to be locally parallel to the immersed surface, and the tangential velocity in the vicinity of the immersed surface is assumed to obey a power-law function of the local immersed surface normal. This approach helps in mimicking the energising effects of turbulent boundary layers without excessive mesh refinement near the immersed surface for suitable choices of the power-law coefficient. Temperature reconstruction is achieved from considerations of temperature variation in compressible thermal boundary layers, and density is estimated by either solving the continuity equation or by interpolation. The turbulence variables are reconstructed using law-of-the-wall-type approach. The application of the outlined immersed boundary method to the simulation of flow control devices is also discussed. Additionally, interpolation procedures for reconstructing the pressure and shear stress at the immersed surface and its application to simple cases are also presented. This information can be useful for comparison with experimental data, performing fluid–structure interaction studies, and also identifying flow-separation and re-attachment locations on the immersed surface.
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TL;DR: This work recognizes the need for additional dissipation in any higher-order Godunov method of this type, and introduces it in such a way so as not to degrade the quality of the results.
3,892 citations
TL;DR: The term immersed boundary (IB) method is used to encompass all such methods that simulate viscous flows with immersed (or embedded) boundaries on grids that do not conform to the shape of these boundaries.
Abstract: The term “immersed boundary method” was first used in reference to a method developed by Peskin (1972) to simulate cardiac mechanics and associated blood flow. The distinguishing feature of this method was that the entire simulation was carried out on a Cartesian grid, which did not conform to the geometry of the heart, and a novel procedure was formulated for imposing the effect of the immersed boundary (IB) on the flow. Since Peskin introduced this method, numerous modifications and refinements have been proposed and a number of variants of this approach now exist. In addition, there is another class of methods, usually referred to as “Cartesian grid methods,” which were originally developed for simulating inviscid flows with complex embedded solid boundaries on Cartesian grids (Berger & Aftosmis 1998, Clarke et al. 1986, Zeeuw & Powell 1991). These methods have been extended to simulate unsteady viscous flows (Udaykumar et al. 1996, Ye et al. 1999) and thus have capabilities similar to those of IB methods. In this review, we use the term immersed boundary (IB) method to encompass all such methods that simulate viscous flows with immersed (or embedded) boundaries on grids that do not conform to the shape of these boundaries. Furthermore, this review focuses mainly on IB methods for flows with immersed solid boundaries. Application of these and related methods to problems with liquid-liquid and liquid-gas boundaries was covered in previous reviews by Anderson et al. (1998) and Scardovelli & Zaleski (1999). Consider the simulation of flow past a solid body shown in Figure 1a. The conventional approach to this would employ structured or unstructured grids that conform to the body. Generating these grids proceeds in two sequential steps. First, a surface grid covering the boundaries b is generated. This is then used as a boundary condition to generate a grid in the volume f occupied by the fluid. If a finite-difference method is employed on a structured grid, then the differential form of the governing equations is transformed to a curvilinear coordinate system aligned with the grid lines (Ferziger & Peric 1996). Because the grid conforms to the surface of the body, the transformed equations can then be discretized in the
3,184 citations
TL;DR: In this paper, the Navier-Stokes equations on a rectangular domain are applied to the simulation of flow around the natural mitral valve of a human heart valve, where the boundary forces are of order h − 1, and because they are sensitive to small changes in boundary configuration, they tend to produce numerical instability.
2,517 citations
TL;DR: In this paper, a second-order accurate, highly efficient method is developed for simulating unsteady three-dimensional incompressible flows in complex geometries, which is achieved by using boundary body forces that allow the imposition of the boundary conditions on a given surface not coinciding with the computational grid.
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TL;DR: In this paper, the Navier-Stokes equations permit the presence of an externally imposed body force that may vary in space and time, and the velocity is used to iteratively determine the desired value.
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