Aeroacoustic Test Cases

The least square-based finite difference-finite volume (LSFD-FV) method has been developed and successfully applied to solve various two-dimensional flow problems with a high-order of accuracy. In this paper, the extension of the LSFD-FV method to the three-dimensional (3D) case on unstructured grids is presented. Different from other existing high-order methods, the LSFD-FV method combines the good features of the least square-based finite difference (LSFD) scheme for derivative approximation and the finite volume (FV) discretization for conservation of physical laws. Within each control cell, a high-order polynomial resultant from a Taylor series expansion is used to approximate the solution in the FV discretization of governing equations, where the derivatives are approximated by the LSFD scheme. As a result, the mesh-free nature of the LSFD scheme endows the LSFD-FV method with the flexibility on unstructured grids. Additionally, the straightforward algorithm of the LSFD scheme and the direct utilization of the Taylor series polynomial make the LSFD-FV method user-friendly and easy to implement. Furthermore, the inviscid and viscous fluxes are simultaneously evaluated by lattice Boltzmann and gas kinetic flux solvers in this work, which avoids additional and complicated treatment for the viscous discretization. Accuracy studies on unstructured hexahedral and tetrahedral grids validate the third-order of accuracy of the 3D LSFD-FV method. Various 3D incompressible and compressible numerical experiments are also presented. The results show that the proposed method enjoys the higher accuracy than the conventional second-order method on the same mesh. When the same accuracy is achieved, the present high-order method has superior computational efficiency to the second-order counterpart.

The results of numerical simulation and comparison with experimental data of the aerodynamic characteristics of a blunt cone are presented. Two authors’ computer codes were used, intended for the numerical integration of the Navier-Stokes and Euler equations on tetrahedral unstructured and multi-block structured computational grids. Alternative numerical models on unstructured grids are analyzed in detail.

The harmonic balance method has proven to be an efficient tool for the study of aeroelastic phenomena associated with blades in turbomachinery components. In the turbomachinery industry it is used, for example, to predict the flutter susceptibility of blades using structured meshes. For the analysis of more complex geometries, like cavities or labyrinth seals, unstructured grids are easier to create than structured ones to accurately model geometric details of these components. With this application in mind, specifically the flutter analysis of labyrinth seals, an existing harmonic balance solver for the unsteady Reynolds averaged Navier-Stokes equations on structured grids has been extended to work efficiently on unstructured grids. Although the harmonic balance algorithm itself is agnostic to the spatial discretization method, as it is only related to the discretization in time, some adaptations are necessary for an efficient implementation. To verify the extensions for unstructured grids, the harmonic balance solver is applied to the flutter analysis of a NACA airfoil exhibiting an oscillating shock-induced separation region. To demonstrate the ability to handle unstructured mixed-element grids, a flutter analysis of a generic labyrinth seal test case on an unstructured grid is performed.

The paper considers methods and algorithms providing the basis for a computer program implementing an axial-symmetric electrostatic version of the particle-in-cell method on unstructured triangular grids. In the presented implementation, the Poisson equation is approximated using the finite volume method. A discrete analog of the Poisson equation is solved by the multigrid method. Charged particle trajectories are calculated using the Boris method. Methods for interpolating electrostatic fields on unstructured grids and obtaining the charge density in the computational domain are considered. Special attention is paid to the specifics of implementing these methods in axisymmetric geometry. The developed computer code is tested on the problem of a flat diode operating in the space charge mode.

High-order level set reinitialization for multiphase flow simulations based on unstructured grids

A high-order accurate flow solution method for quadrilateral elements is developed and tested. The method employs the flux reconstruction (FR) approach proposed by Huynh. Ideal orders of accuracy are achieved for several problems on structured-based grids while some deterioration is observed on purely unstructured grids. Cares for curved wall boundary are also shown. The localized artificial diffusivity (LAD) method is incorporated to capture discontinuities that is crucial for compressible flow simulations. The FR+LAD works very well for 1D test cases but multi-dimensional shock problems requires further modifications to confine the artificial diffusivity to the shock location. Hybrid scheme of the FR and finite difference method taking advantage of 1D-feature alleviates the instability. I. Introduction Expanding demands for the computational fluid dynamics (CFD) requires more reliable numerical schemes. Specifically, turbulent flow simulations, acoustic simulation, combustion simulations and their combined problems. The key words in such simulations may be high accuracy and high resolution. In structured grid CFD, a compact finite difference scheme satisfies both requirements at higher level than existing other methods. If we put more emphasis on easier handling of complex geometries and flow-data dependent grid generation (grid adaptation), then unstructured grid method should also be explored and it should depart from 2nd-order scheme with limiter. Recent efforts in this area are development of the discontinuous Galerkin (DG) method, 1,2 the spectral finite volume (SV) method 3 and the staggered-grid multi-domain method spectral finite difference (SG) method 4,5 and its evolutional method called a spectral difference method. 6 The common and maybe the only way for those unstructured methods is to add degrees of freedom in each cell to achieve high order since the wide stencil of the original grid is not possible due to unstructured nature. The ENO-type method that uses original degrees of freedom in the grids and extends adaptive stencils to the flow solutions is also explored but the difficulty of extending stencils due to undirectional nature of unstructured grids and the unsuitability for parallel computing prohibits wide applications. A flux reconstruction (FR) scheme 7,8 studied in the paper is the new one among the former group. It uses differential form of conservation laws like the SD method but it is more general and includes equivalent counter part of the schemes in the group. In this paper, the performance of the FR is tested by a newly developed Navier-Stokes solver. Realistic flow applications of the FR in the Navier-Stokes equations are seldom seen since it is relatively new scheme. The Localized artificial diffusivity (LAD) 9–13 is incorporated for the shock capturing in the FR. The last item is motivated by the challenge and success of combining the SD and LAD in the recent study. 11,12 Wang 14 developed the lifting collocation penalty (LCP) method to extend the FR to triangular or tetrahedral grids and applied the LCP-FR combined method for hybrid unstructured grids. In the present study, only quadrilateral cells are treated to directly apply the LAD method that was developed on structured grids. The shock capturing by the FR+LAD high order scheme is tried.

Adaptive numerical dissipation control for high-order k-exact reconstruction schemes on vertex-centered unstructured grids using artificial neural networks

Development and verification of an unresolved CFD-DEM method applicable to different-sized grids

In this paper we focus on the application of a higher-order finite volume method for the resolution of Computational Aeroacoustics problems. In particular, we present the application of a finite volume method based in Moving Least Squares approximations in the context of a hybrid approach for low Mach number flows. In this case, the acoustic and aerodynamic fields can be computed separately. We focus on two kinds of computations: turbulent flow and aeroacoustics in complex geometries. Both fields require very accurate methods to capture the fine features of the flow, small scales in the case of turbulent flows and very low-amplitude acoustic waves in the case of aeroacoustics. On the other hand, the use of unstructured grids is interesting for real engineering applications, but unfortunately, the accuracy and efficiency of the numerical methods developed for unstructured grids is far to reach the performance of those methods developed for structured grids. In this context, we propose the FV-MLS method as a tool for accurate CAA computations on unstructured grids.

The primitive variable formulation of the moist hydrostatic equations conserves mass and moist total energy due to the property that the divergence and gradient operators are adjoints. Any compatible numerical method, which has a discrete analog of this property will conserve a discrete mass and total energy. We demonstrate this using aqua-planet simulations performed with CAM-HOMME (NCAR’s Community Atmospheric Model with the High-Order Method Modeling Environment dynamical core). CAM-HOMME uses a compatible numerical method on arbitrary unstructured quadrilateral grid. The equations described here are the full set of dynamical equations used by CAM. Aqua-planet simulations use the full suite of physics parametrizations as well. The only simplification is the use of idealized surface conditions. We report on the magnitude of the total energy budget in the dynamical core including estimates for the non-adiabatic processes. The practice of fixing dry total energy as opposed to the conserved total moist energy is shown to generate a forcing of − 0. 56 W/m2.

Multidimensional upwind convection schemes for flow in porous media on structured and unstructured quadrilateral grids

Large-Eddy Simulation of wind turbines wakes including geometrical effects

A 3-D Navier-Stokes CFD code using unstructured grid has been developed for the purpose of practical use. Accuracy, robustness, efficiency, applicability to wide range of flow speeds and convenient grid generation have been emphasized. Two test cases are presented: a square-sectioned U-bends and a serpentine passage. It is demonstrated that the present code satisfactorily predicts the flow and heat transfer in the bend with moderate curvature. It is also indicated that the current code shows poor agreement with experiments in the bend with strong curvature because of the simple model for the viscous sublayer.

Biodegrading plumes in groundwater are often typified by relatively reactive zones around the fringes and less reactive zones in the core. A high degree of refinement is required at the fringes if a model is to be of use in improving the conceptual understanding of plumes. Two strategies for dealing with the potentially high computational demands are (i) parallel processing, where the workload is shared between multiple processors, and (ii) locally adaptive remeshing, where a refined area of the grid tracks the moving plume fringes through the domain. The partial differential equation toolbox, UG (Unstructured Grids) offers advanced numerical tools including adaptive remeshing, sparse matrix storage schemes, and multigrid solvers. It embraces many of these features within a parallel processing environment. This paper reports on a recent development of UG to simulate field scale reactive biogeochemistry including Monod kinetics, NAPL dissolution, mineral precipitation/dissolution and ion exchange. The non-linear multicomponent reactive transport system is solved with the fully coupled method. Test cases have been used for verification of the new capability. The paper illustrates an application to a 3D field site. It is demonstrated that both adaptive remeshing and parallel processing can improve efficiency and in turn facilitate the incorporation of a more complex set of species and reactions such that understanding of plume processes is enhanced.

Three-dimensional aerodynamic computations on unstructured grids using a Newton–Krylov approach