In this paper, a novel immersed boundary method is developed, validated, and applied. Through devising a second-order three-step flow reconstruction scheme, the proposed method is able to enforce the Dirichlet, Neumann, Robin, and Cauchy boundary conditions in a straightforward and consistent manner. Equipped with a fluid-solid coupling framework that integrates high-order temporal and spatial discretization schemes, numerical experiments concerning flow involving stationary and moving objects, convex and concave geometries, no-slip and slip wall boundary conditions, as well as subsonic and supersonic motions are conducted to validate the method. It is demonstrated that the proposed method can provide efficient, accurate, and robust boundary treatment for solving flow with arbitrarily irregular and moving geometries on Cartesian grids.
This paper sums up some recent validations of an immersed boundary method for compressible flow simulations. It has been already shown that this method is able to provide accurate results without meshing effort around more or less complex geometries. Here, the authors focus on several simple test cases to assess the application range of the method. From subsonic to hypersonic flows, from steady to large-eddy unsteady simulations, in 2D or 3D, results are compared to classical simulations with body-fitted meshes and experiment. Moreover, the use of an efficient Navier-Stokes solver for all the …
An immersed-boundary (IB) method is proposed and applied in the gas-kinetic BGK scheme to simulate incompressible/compressible viscous flow with stationary/moving boundary. In present method the ghost-cell technique is adopted to fulfill the boundary condition on the immersed boundary. A novel idea "local boundary determination" is put forward to identify the ghost cells, each of which may have several different ghost-cell constructions corresponding to different boundary segments, thus eliminating the singularity of the ghost cell. Furthermore, the so-called "fresh-cell" problem when implemen…
In the present study, a discrete forcing Immersed Boundary Method (IBM) is proposed for the numerical simulation of high-speed flow problems including heat exchange. The flow field is governed by the compressible Navier-Stokes equations, which are resolved by using the open source library OpenFOAM. The numerical solver is modified to include source terms in the momentum equation and in the energy equation, which account for the presence of the immersed body. The method is validated on some benchmark test cases dealing with forced convection problems and moving immersed bodies. The results obta…
We introduce an immersed high-order discontinuous Galerkin method for solving the compressible Navier-Stokes equations on non-boundary-fitted meshes. The flow equations are discretised with a mixed discontinuous Galerkin formulation and are advanced in time with an explicit time marching scheme. The discretisation meshes may contain simplicial (triangular or tetrahedral) elements of different sizes and need not be structured. On the discretisation mesh the fluid domain boundary is represented with an implicit signed distance function. The cut-elements partially covered by the solid domain are …
We derive a mathematical model and the corresponding computational scheme to study deflection of a two-dimensional elastic cantilever beam immersed in a channel, where one end of the beam is fixed to the channel wall. The immersed boundary method has been employed to simulate numerically the fluid-structure interaction problem. We investigate how variations in physical and numerical parameters change the effective material properties of the elastic beam and compare the results qualitatively with linear beam theory. We also pay careful attention to "corner effects" -- irregularities in beam sha…
We report development and application of a fluid-structure interaction (FSI) solver for compressible flows with large-scale flow-induced deformation of the structure. The FSI solver utilizes partitioned approach to strongly couple a sharp-interface immersed boundary method based flow solver with an open-source finite-element structure dynamics solver. The flow solver is based on a higher-order finite-difference method on Cartesian grid and employs ghost-cell methodology to impose boundary conditions on the immersed boundary. A higher-order accuracy near the immersed boundary is achieved by com…
We present a new higher-order accurate finite difference explicit jump Immersed Interface Method (HEJIIM) for solving two-dimensional elliptic problems with singular source and discontinuous coefficients in the irregular region on a compact Cartesian mesh. We propose a new strategy for discretizing the solution at irregular points on a nine point compact stencil such that the higher-order compactness is maintained throughout the whole computational domain. The scheme is employed to solve four problems embedded with circular and star shaped interfaces in a rectangular region having analytical s…
We present an approach for numerically simulating the dynamics of flexible fibers in a three-dimensional shear flow using a scalable immersed boundary (IB) algorithm based on Guermond and Minev's pseudo-compressible fluid solver. The fibers are treated as one-dimensional Kirchhoff rods that resist stretching, bending, and twisting, within the generalized IB framework. We perform a careful numerical comparison against experiments on single fibers performed by S. G. Mason and co-workers, who categorized the fiber dynamics into several distinct orbit classes. We show that the orbit class may be d…
Most fluid flow problems that are vital in engineering applications involve at least one of the following features: turbulence, shocks, and/or material interfaces. While seemingly different phenomena, these flows all share continuous generation of high wavenumber modes, which we term the '$k_\infty$ irregularity.' In this work, an inviscid regularization technique called 'observable regularization' is proposed for the simulation of two-phase compressible flows. The proposed approach regularizes the equations at the level of the partial differential equation and as a result, any numerical metho…
The goal of this report is to present the final project conducted in order to fulfill the requirements of the M.Sc. degree at the Department of Mechanical Engineering, Ben-Gurion University (BGU) of the Negev. The project comprises theoretical research investigating natural convection compressible flow with high temperature differences and with complex geometries. The research motivation comes from long-term research investigating and simulating the steady state and transient multiphase flow regimes existing in the reactor core, that was established by the Soreq Nuclear Center. The main object…
We investigate flows interacting with a square and a fractal shape multi-scale structures in the compressible regime for Mach numbers at subsonic and supersonic upstream conditions using large-eddy-simulations (LES). We also aim at identifying similarities and differences that these interactions have with corresponding interactions in the canonical incompressible flow problem. To account for the geometrical complexity associated with the fractal structures, we apply an immersed boundary method to model the no-slip boundary condition at the solid surfaces, with adequate mesh resolution in the v…
We present a new implicit higher-order finite element (FE) approach to efficiently model compressible multicomponent fluid flow on unstructured grids and in fractured porous subsurface formations. The scheme is sequential implicit: pressures and fluxes are updated with an implicit Mixed Hybrid Finite Element (MHFE) method, and the transport of each species is approximated with an implicit second-order Discontinuous Galerkin (DG) FE method. Discrete fractures are incorporated with a cross-flow equilibrium approach. This is the first investigation of all-implicit higher-order MHFE-DG for unstruc…
In this paper, the compact gas-kinetic scheme for compressible flow is extended to hybrid unstructured mesh. Based on both cell-averaged flow variables and their gradients updated from time accurate gas evolution model at cell interfaces, a compact third-order least-square-constrained reconstruction can be obtained on unstructured mesh and a multi-resolution WENO reconstruction is adopted in case of discontinuous solutions. Moreover, a compression factor for the cell-averaged gradients is proposed to take into account the possible discontinuity in flow variables at cell interface, which signif…
Simulations of a supersonic, premixed, reacting flow over a wedge were performed to investigate the effect of a boundary layer on the wedge surface on ignition and stability of oblique detonation waves (ODWs). Two computational domains were used: one containing a wedge of a single angle with a straight after-body, and the other containing a double-angle wedge geometry. Both domains were channels with a supersonic inflow of stoichiometric hydrogen-air and a nonreflecting outflow, and the wedge was modeled using an immersed boundary method. The compressible reactive Navier-Stokes equations were …
We introduce an open-source and unified framework for transition analysis for laminar boundary layer natural transition at transonic conditions and over complex geometries, where surface irregularities may be present. Different computational tools are integrated in the framework, and therefore overcomes the difficulties of two separate and usually quite disparate processes when using $e^N$ method for transition analysis. To generate a baseflow with desired pressure distribution, appropriate pressure compatible inflow boundary condition needs to be developed and enforced. We first derive the sy…
