A novel immersed boundary procedure for flow and heat simulations with moving boundary

This article describes a novel immersed boundary procedure for computing the flow and heat transfer problems with moving and complex boundary. Although the immersed boundary techniques have been successfully implemented to these flow and heat simulations, a frequently encountered drawback of this method is the relatively low accuracy proximate to the boundary due to the spreading of forcing function or the interpolation scheme. In this study, we propose a moving-grid process under the arbitrary Lagrangian-Eulerian framework to reduce the numerical diffusion near the immersed boundary. The incompressible Navier-Stokes equations are discretized spatially using unstructured finite element method, and advanced temporally by an operator-splitting scheme. The methodology is validated by the simulations of flow induced by an oscillating cylinder in a free stream. The capability of the proposed method is further demonstrated by good predictions of flow passing the rotating fan in a channel and also flow driven by two independent rotating fans in a circular cavity.     

Time-accurate Navier-Stokes simulation of vortex convection using an unstructured dynamic mesh procedure

A two-dimensional Navier-Stokes flow solver is developed for the simulation of unsteady flows on unstructured adaptive meshes. The solver is based on a second-order accurate implicit time integration using a point Gauss-Seidel relaxation scheme and a dual time-step subiteration. A vertex-centered, finite-volume discretization is used in conjunction with Roe’s flux-difference splitting. The Spalart-Allmaras one equation model is employed for the simulation of turbulence. An unsteady solution-adaptive dynamic mesh scheme is used by adding and deleting mesh points to take account of spatial and temporal variations of the flowfield. Unsteady viscous flow for a traveling vortex in a free stream is simulated to validate the accuracy of the dynamic mesh adaptation procedure. Flow around a circular cylinder and two blade-vortex interaction problems are investigated for demonstration of the present method. Computed results show good agreement with existing experimental and computational results. It was found that unsteady time-accurate viscous flows can be accurately simulated using the present unstructured dynamic mesh adaptation procedure.     

An algorithm for velocity calculation in close proximity to body surfaces in panel methods

To model incompressible flow over a body of arbitrary geometry when using vortex methods, it is necessary to construct an irrotational field to impose the impermeability condition at the surface of the object. In order to achieve this impermeability, this paper uses a boundary integral equation based on the single-layer representation for the velocity potential. Specifically, we formulate this exterior Neumann problem in terms of a source/sink boundary integral equation. The solution to this integral equation is then coupled with an interpolation procedure which smoothes the transition between near-wall and interior regimes. We describe the numerical scheme embedding this strategy and discuss its accuracy and efficiency. For validation purposes, we consider the potential and vortical flow over a circular cylinder, for which an analytical solution and the commonly used method of images are available.     

A collocated finite volume embedding method for simulation of flow past stationary and moving body

A simple and conservative numerical scheme is introduced in this paper to simulate unsteady flow around stationary and moving body. Based on the embedding method (immersed boundary (IB) + volume of fluid (VOF)) implemented in the finite-volume framework, flow past the arbitrarily complex geometry can be readily computed on any existing mesh system. Flow variables stored at cell centers, including those residing within the immersed body, are computed where the induced effect on the flow due to the immersed body is realised via a simple acceleration term (forcing function) derived based on the VOF value. In the current work, an identical VOF value is used for all momentum equations, in contrast to that of the pre-existing method, whereby numerical interpolation is required. The method is verified with a number of flow cases, including flow in a 2D square cavity, flow past a stationary and oscillating cylinder and flow induced by a flapping ellipse in an enclosure.     

A numerical simulation of inertial waves in a rotating fluid

Inertial waves in a fluid-filled rotating cylinder are studied using a numerical simulation. A perturbation applied along the centerline at the midplane of a right circular cylinder is used to excite these internal waves. A primitive variable, time-marching finite difference solution of the linearized axisymmetric governing equations is used to obtain the flow and pressure fields. Results compare well with theoretical predictions and are displayed graphically.     

A coarse-grid projection method for accelerating incompressible MHD flow simulations

Coarse grid projection (CGP) is a multiresolution technique for accelerating numerical calculations associated with a set of nonlinear evolutionary equations along with stiff Poisson’s equations. In this article, we use CGP for the first time to speed up incompressible magnetohydrodynamics (MHD) flow simulations. Accordingly, we solve the nonlinear advection–diffusion equation on a fine mesh, while we execute the electric potential Poisson equation on the corresponding coarsened mesh. Mapping operators connect two grids together. A pressure correction scheme is used to enforce the incompressibility constrain. The study of incompressible flow past a circular cylinder in the presence of Lorentz force is selected as a benchmark problem with a fixed Reynolds number but various Stuart numbers. We consider two different situations. First, we only apply CGP to the electric potential Poisson equation. Second, we apply CGP to the pressure Poisson equation as well. The maximum speed-up factors achieved here are approximately 3 and 23, respectively, for the first and second situations. For the both situations, we examine the accuracy of velocity and vorticity fields as well as the lift and drag coefficients. In general, the results obtained by CGP are in an excellent to reasonable range of accuracy. The CGP results are significantly more accurate compared to the numerical simulations of the advection–diffusion and electric potential Poisson equations on pure coarse scale grids.

     

A numerical study of flow past a cylinder with cross flow and inline oscillation

Two-dimensional fluid flow around an oscillating circular cylinder is studied numerically at different values of oscillation frequency and amplitude. A novel finite element method which uses discretization along the characteristic line is used for simulation. The solver is coupled to a mesh movement scheme using the Arbitrary Lagrangian-Eulerian (ALE) formulation to account for body motion in the flow field. Two cases of cylinder motion have been studied, cross flow and inline oscillation. In both cases, occurrence of lock on is investigated and the bounds of the lock on region are determined. A comparison of the numerical results with the experimental data indicates that 2D simulation is valid up to Re = 300. Beyond that, 3D effects appear. By using flow visualization, effect of a cylinder oscillation on the flow field and wake pattern has been studied. Also, variation of the mean drag coefficient against the oscillation parameters is discussed. The numerical results are in good agreement with the experimental data available in the literature.     

A comprehensive generalized mesh system for CFD applications

The numerical approaches used for the solution of governing equations of fluid flow are dictated highly by the topology of the domain discretization. Two of the most commonly used discretization approaches are the structured and unstructured topologies. This paper describes the discretization of the domain using generalized elements with an arbitrary number of nodes to combine the advantages of both the structured and unstructured methodologies. Numerical algorithms for the solution of the governing equations for generalized mesh, an approach for handling mesh movement applicable to rotating machineries, and the application of this framework for overset meshes to handle moving body problems are discussed. A library-based approach has been adopted for the implementation of overset capability for the framework. The results from the application of this framework for various applications are presented.     

Incompressible flow computations over moving boundary using a novel upwind method

In this paper a novel method for simulating unsteady incompressible viscous flow over a moving boundary is described. The numerical model is based on a 2D Navier–Stokes incompressible flow in artificial compressibility formulation with Arbitrary Lagrangian Eulerian approach for moving grid and dual time stepping approach for time accurate discretization. A higher order unstructured finite volume scheme, based on a Harten Lax and van Leer with Contact (HLLC) type Riemann solver for convective fluxes, developed for steady incompressible flow in artificial compressibility formulation by Mandal and Iyer (AIAA paper 2009-3541), is extended to solve unsteady flows over moving boundary. Viscous fluxes are discretized in a central differencing manner based on Coirier’s diamond path. An algorithm based on interpolation with radial basis functions is used for grid movements. The present numerical scheme is validated for an unsteady channel flow with a moving indentation. The present numerical results are found to agree well with experimental results reported in literature.     

Mesh deformation using radial basis functions for gradient-based aerodynamic shape optimization

Gradient-based aerodynamic shape optimization using computational fluid dynamics (CFD), and time dependent problems in aeroelasticity, that is, coupled calculations between computational structural mechanics (CSM) and CFD, require repeated deformations of the CFD mesh.An interpolation scheme, based on radial basis functions (RBF), is devised in order to propagate the deformations from the boundaries to the interior of the CFD mesh. This method can lower the computational costs due to the deformation of the mesh, in comparison with the usual Laplace smoothing. Moreover, the algorithm is independent of the mesh connectivities. Therefore, structured and unstructured meshes are equally treated as well as hybrid meshes.The application of this interpolation scheme in problems of aerodynamic shape optimization is also carefully investigated. When the optimization is executed by a gradient-based algorithm the cost function is differentiated with respect to the design parameters in order to obtain the gradient. The gradient is most efficiently and accurately calculated by solving a certain adjoint equation derived from the discretized flow equations. The calculation of the gradient, which is detailed in this presentation, involves the Jacobian matrix of the mesh deformation.Finally, we present the results of an optimization of the ONERA M6 wing at transonic speed using the interpolation algorithm. The results are used for comparison with another technique of mesh deformation. The quality of the mesh obtained by the new algorithm, and the interpolation error, are analyzed with respect to the parameters of the interpolation scheme: the type of RBF, the RBF’s shape parameter, and the sets of control points.     

A unifying grid approach for solving potential flows applicable to structured and unstructured grid configurations

In this study, an efficient numerical method is proposed for unifying the structured and unstructured grid approaches for solving the potential flows. The new method, named as the “alternating cell directions implicit - ACDI”, solves for the structured and unstructured grid configurations equally well. The new method in effect applies a line implicit method similar to the Line Gauss Seidel scheme for complex unstructured grids including mixed type quadrilateral and triangle cells. To this end, designated alternating directions are taken along chains of contiguous cells, i.e. ‘cell directions’, and an ADI-like sweeping is made to update these cells using a Line Gauss Seidel like scheme. The algorithm makes sure that the entire flow field is updated by traversing each cell twice at each time step for unstructured quadrilateral grids that may contain triangular cells. In this study, a cell-centered finite volume formulation of the ACDI method is demonstrated. The solutions are obtained for incompressible potential flows around a circular cylinder and a forward step. The results are compared with the analytical solutions and numerical solutions using the implicit ADI and the explicit Runge-Kutta methods on single-and multi-block structured and unstructured grids. The results demonstrate that the present ACDI method is unconditionally stable, easy to use and has the same computational performance in terms of convergence, accuracy and run times for both the structured and unstructured grids.     

High Order Accurate Solution of Flow Past a Circular Cylinder

A high order method is applied to time-dependent incompressible flow around a circular cylinder geometry. The space discretization employs compact fourth-order difference operators. In time we discretize with a second-order semi-implicit scheme. A large linear system of equations is solved in each time step by a combination of outer and inner iterations. An approximate block factorization of the system matrix is used for preconditioning. Well posed boundary conditions are obtained by an integral formulation of boundary data including a condition on the pressure. Two-dimensional flow around a circular cylinder is studied for Reynolds numbers in the range 7 ≤ R ≤ 180. The results agree very well with the data known from numerical and experimental studies in the literature.     

On some approaches to solve CFD problems

This paper presents two efficient methods for spatial flows calculations. In order to simulate of incompressible viscous flows, a second-order accurate scheme with an incomplete LU decomposed implicit operator is developed. The scheme is based on the method of artificial compressibility and Roe flux-difference splitting technique for the convective terms. The numerical algorithm can be used to compute both steady-state and time-dependent flow problems. The second method is developed for modeling of stationary compressible inviscid flows. This numerical algorithm is based on a simple flux-difference splitting into physical processes method and combines a multi level grid technology with a convergence acceleration procedure for internal iterations. The capabilities of the methods are illustrated by computations of steady-state flow in a rotary pump, unsteady flow over a circular cylinder and stationary subsonic flow over an ellipsoid.     

A high-resolution method for the depth-integrated solute transport equation based on an unstructured mesh

This paper presents a high-resolution numerical method for solving mass transport problems involving advection and anisotropic diffusion in shallow water based on unstructured mesh. An alternating operator-splitting technique is adopted to advance the numerical solution with advection and diffusion terms solved separately in two steps. By introducing a new r-factor into the Total Variation Diminishing (TVD) limiter, an improved finite-volume method is developed to solve the advection term with significant reduction of numerical diffusion and oscillation errors. In addition, a coordinate transformation is introduced to simplify the diffusion term with the Green-Gauss theorem used to deal with the anisotropic effect based on unstructured mesh. The new scheme is validated against three benchmark cases with separated and combined advection and diffusion transport processes involved. Results show that the scheme performs better than existing methods in predicting the advective transport, particularly when a sharp concentration front is in presence. The model also provides a sound solution for the anisotropic diffusion phenomenon. Anisotropic diffusion has been largely neglected by existing flow models based on unstructured mesh, which usually treat the diffusion process as being isotropic for simplicity. Based on the flow field provided by the ELCIRC model, the developed transport model was successfully applied to simulate the transport of a hypothetical conservative tracer in a bay under the influence of tides.     

A parallel multigrid solver for incompressible flows on computing architectures with accelerators

An efficient parallel multigrid pressure correction algorithm is proposed for the solution of the incompressible Navier–Stokes equations on computing architectures with acceleration devices. The pressure correction procedure is based on the numerical solution of a Poisson-type problem, which is discretized using a fourth-order finite difference compact scheme. Since this is the most time-consuming part of the solver, we propose a parallel pressure correction algorithm using an iterative method based on a block cyclic reduction solution method combined with a multigrid technique. The grid points are numbered with respect to the red–black ordering scheme for the parallel Gauss–Seidel smoother. These parallelization techniques allow the execution of the entire simulation computations on the acceleration device, minimizing memory communication costs. The realization is developed using the OpenACC API, and the numerical method is demonstrated for the solution of two classical incompressible flow test problems. The first is the two-dimensional lid-driven cavity problem over equal mesh sizes while the other is the Stokes boundary layer, which is a decent benchmark problem for unequal mesh spacing. The effect of several multigrid components on modern and legacy acceleration architectures is examined. Eventually the performance investigation demonstrates that the proposed parallel multigrid solver achieves an acceleration of more than 10\(\times \) over the sequential solver and more than 4\(\times \) over multi-core CPU only realizations for all tested accelerators.     

Calculation of hydrodynamic forces acting on a submerged moving object using immersed boundary method

General formulae are derived to calculate the hydrodynamic force acting on a solid object, either stationary or in motion, when an immersed boundary (IB) method is used to simulate the flow around the object. These formulae explore the fact that the imposed force term in the IB method contributes to the force applied by the object on the external fluid as well as the unsteady flow inside the virtual domain which is occupied by the object. These formulae are particularly important when the object in unsteady motion is solved in an inertial coordinate system. The formulae are adopted in the present two-dimensional (2D) numerical model, in which a SIMPLEC-type two-step computational scheme is introduced to solve the Navier-Stokes (N-S) equations. Several case studies, including the simulation of the vortex-induced vibration (VIV) of a circular cylinder, are carried out in this work. The agreement of the predicted results with the experimental and numerical data reported by other researchers proves the significance of these formulae.     

A numerical investigation of fluid flow over a rotating cylinder with cross flow oscillation

This paper studies a two-dimensional incompressible viscous flow past a rotating cylinder with cross flow oscillation using a finite element method based on the characteristic based split (CBS) algorithm to solve governing equations including full Navier–Stokes and continuity equations. Dynamic unstructured triangular grid is used employing lineal and torsional spring analogy which is coupled with the solver by an Arbitrary Lagrangian–Eulerian (ALE) formulation. After verifying the accuracy of the numerical code, simulations are conducted for the flow past a rotating cylinder with cross flow oscillation at moderate Reynolds numbers of 50, 100, and 200 considering different non-dimensional rotational speeds based on the free-stream velocity in the range 0–2.5, and various oscillating amplitudes and frequencies. Effects of the oscillation and rotation of the cylinder on the vortex shedding both in lock-on and non-lock-on regions, the mean drag and lift coefficients, and the Strouhal number are investigated in detail. It is found that similar to the fixed cylinder beyond a critical non-dimensional rotational speed the vortex shedding is highly suppressed. In addition, by increasing the rotational speed of the cylinder, the lift coefficient increases while decreasing the drag coefficient. However, in the vortex lock-on region both the lift and the drag coefficients increase significantly.     

A finite volume method to solve the 3D Navier–Stokes equations on unstructured collocated meshes

A new method to solve the Navier–Stokes equations for incompressible viscous flows and the transport of a scalar quantity is proposed. This method is based upon a fractional time step scheme and the finite volume method on unstructured meshes. The governing equations are discretized using a collocated, cell-centered arrangement of velocity and pressure. The solution variables are stored at the cell-circumcenters. Theoretical results and numerical properties of the scheme are provided. Predictions of lid-driven cavity flow, flows past a cylinder and heat transport in a cylinder are performed to validate the method.     

A virtual test facility for the efficient simulation of solid material response under strong shock and detonation wave loading

A virtual test facility (VTF) for studying the three-dimensional dynamic response of solid materials subject to strong shock and detonation waves has been constructed as part of the research program of the Center for Simulating the Dynamic Response of Materials at the California Institute of Technology. The compressible fluid flow is simulated with a Cartesian finite volume method and treating the solid as an embedded moving body, while a Lagrangian finite element scheme is employed to describe the structural response to the hydrodynamic pressure loading. A temporal splitting method is applied to update the position and velocity of the boundary between time steps. The boundary is represented implicitly in the fluid solver with a level set function that is constructed on-the-fly from the unstructured solid surface mesh. Block-structured mesh adaptation with time step refinement in the fluid allows for the efficient consideration of disparate fluid and solid time scales. We detail the design of the employed object-oriented mesh refinement framework AMROC and outline its effective extension for fluid–structure interaction problems. Further, we describe the parallelization of the most important algorithmic components for distributed memory machines and discuss the applied partitioning strategies. As computational examples for typical VTF applications, we present the dynamic deformation of a tantalum cylinder due to the detonation of an interior solid explosive and the impact of an explosion-induced shock wave on a multi-material soft tissue body.     

结构变形对整流罩分离轨迹的影响

为研究弹性体在稠密大气中的分离问题,基于非结构网格,采用运动网格与局部网格重构相结合的方法求解大位移相对运动的流场,并耦合6自由度刚体运动方程得到整流罩的运动.非定常流动方程使用格心有限体积法进行空间离散,并运用LU-SGS进行求解.应用标准算例验证该方法的准确性,并用于某整流罩飞行轨迹的计算.结果表明结构变形可能会使...