Multi-rate time integration on overset meshes

In the computational fluid dynamic simulation of problems with complex geometries or multiscale spatio-temporal features, overset meshes can be effectively used. However, in the case of overset problems in which one or more of the meshes vary significantly in resolution, standard explicit time integrators limit the maximum allowable timestep across the entire simulation domain to that of the finest mesh, per the well-known Courant-Friedrichs-Lewy (CFL) condition. What therefore results is a potentially high amount of computational work that theoretically need not be performed on the grids with coarser resolution and a commensurately larger timestep. With the targeted use of multi-rate time integrators, separate meshes can be marched at independent rates in time to avoid wasteful computation while maintaining accuracy and stability. This work features the application of such integrators (specifically, multi-rate Adams-Bashforth (MRAB) integrators) to the simulation of overset mesh-described problems using a parallel Fortran code. The thesis focuses on the overarching mathematical theory, implementation via code generation, proof of numerical accuracy and stability, and demonstration of serial and parallel performance capabilities. Specifically, the results of this study directly indicate the numerical efficacy of MRAB integrators, outline a number of outstanding code challenges, demonstrate the expected reduction in time enabled by MRAB, and emphasize the need for proper load balancing through spatial decomposition in order for parallel runs to achieve the predicted time-saving benefit

Investigation of mixed element hybrid grid-based CFD methods for rotorcraft flow analysis

Accurate first-principles flow prediction is essential to the design and development of rotorcraft, and while current numerical analysis tools can, in theory, model the complete flow field, in practice the accuracy of these tools is limited by various inherent numerical deficiencies. An approach that combines the first-principles physical modeling capability of CFD schemes with the vortex preservation capabilities of Lagrangian vortex methods has been developed recently that controls the numerical diffusion of the rotor wake in a grid-based solver by employing a vorticity-velocity, rather than primitive variable, formulation. Coupling strategies, including variable exchange protocols are evaluated using several unstructured, structured, and Cartesian-grid Reynolds Averaged Navier-Stokes (RANS)/Euler CFD solvers. Results obtained with the hybrid grid-based solvers illustrate the capability of this hybrid method to resolve vortex-dominated flow fields with lower cell counts than pure RANS/Euler methods

Computational Simulations of a Mach 0.745 Transonic Truss-Braced Wing Design

A joint effort between the NASA Ames and Langley Research Centers was undertaken to analyze the Mach 0.745 variant of the Boeing Transonic Truss-Braced Wing (TTBW) Design. Two different flow solvers, LAVA and USM3D, were used to predict the TTBW flight performance. Sensitivity studies related to mesh resolution and numerical schemes were conducted to define best practices for this type of geometry and flow regime. Validation efforts compared the numerical simulation results of various modeling methods against experimental data taken from the NASA Ames 11-foot Unitary Wind Tunnel experimental data. The fidelity of the computational representation of the wind tunnel experiment, such as utilizing a porous wall boundary condition to model the ventilated test section, was varied to examine how different tunnel effects influence CFD predictions. LAVA and USM3D results both show an approximate 0.5 angle of attack shift from experimental lift curve data. This drove an investigation that revealed that the trailing edge of the experimental model was rounded in comparison to the CAD model, due to manufacturing tolerances, which had not been accounted for in the initial simulations of the experiment. Simulating the TTBW with an approximation of this rounded trailing-edge reduces error by approximately 60%. An accurate representation of the tested TTBW geometry, ideally including any wing twists and deflections experienced during the test under various loading conditions, will be necessary for proper validation of the CFD

High-fidelity Multidisciplinary Sensitivity Analysis and Design Optimization for Rotorcraft Applications

A multidisciplinary sensitivity analysis of rotorcraft simulations involving tightly coupled high-fidelity computational fluid dynamics and comprehensive analysis solvers is presented and evaluated. A sensitivity-enabled fluid dynamics solver and a nonlinear flexible multibody dynamics solver are coupled to predict aerodynamic loads and structural responses of helicopter rotor blades. A discretely consistent adjoint-based sensitivity analysis available in the fluid dynamics solver provides sensitivities arising from unsteady turbulent flows and unstructured dynamic overset meshes, while a complex-variable approach is used to compute structural sensitivities with respect to aerodynamic loads. The multidisciplinary sensitivity analysis is conducted through integrating the sensitivity components from each discipline of the coupled system. Accuracy of the coupled system is validated by conducting simulations for a benchmark rotorcraft model and comparing solutions with established analyses and experimental data. Sensitivities of lift computed by the multidisciplinary sensitivity analysis are verified by comparison with the sensitivities obtained by complex-variable simulations. Finally the multidisciplinary sensitivity analysis is applied to a constrained gradient-based design optimization for a HART-II rotorcraft configuration

A Discontinuous Galerkin Chimera scheme

The Chimera overset method is a powerful technique for modeling fluid flow associated with complex engineering problems using structured meshes. The use of structured meshes has enabled engineers to employ a number of high-order schemes, such as the WENO and compact differencing schemes. However, the large stencil associated with these schemes can significantly complicate the inter-grid communication scheme and hole cutting procedures. This paper demonstrates a methodology for using the Discontinuous Galerkin (DG) scheme with Chimera overset meshes. The small stencil of the DG scheme makes it particularly suitable for Chimera meshes as it simplifies the inter-grid communication scheme as well as hole cutting procedures. The DG-Chimera scheme does not require a donor interpolation method with a large stencil because the DG scheme represents the solution as cell local polynomials. The DG-Chimera method also does not require the use of fringe points to maintain the interior stencil across inter-grid boundaries. Thus, inter-grid communication can be established as long as the receiving boundary is enclosed by or abuts the donor mesh. This makes the inter-grid communication procedure applicable to both Chimera and zonal meshes. Details of the DG-Chimera scheme are presented, and the method is demonstrated on a set of two-dimensional inviscid flow problems

Study of interpolation methods for high-accuracy computations on overlapping grids

Overset strategy can be an efficient way to keep high-accuracy discretization by decomposing a complex geometry in topologically simple subdomains. Apart from the grid assembly algorithm, the key point of overset technique lies in the interpolation processes which ensure the communications between the overlapping grids. The family of explicit Lagrange and optimized interpolation schemes is studied. The a priori interpolation error is analyzed in the Fourier space, and combined with the error of the chosen discretization to highlight the modification of the numerical error. When high-accuracy algorithms are used an optimization of the interpolation coefficients can enhance the resolvality, which can be useful when high-frequency waves or small turbulent scales need to be supported by a grid. For general curvilinear grids in more than one space dimension, a mapping in a computational space followed by a tensorization of 1-D interpolations is preferred to a direct evaluation of the coefficient in the physical domain. A high-order extension of the isoparametric mapping is accurate and robust since it avoids the inversion of a matrix which may be ill-conditioned. A posteriori error analyses indicate that the interpolation stencil size must be tailored to the accuracy of the discretization scheme. For well discretized wavelengthes, the results show that the choice of a stencil smaller than the stencil of the corresponding finite-difference scheme can be acceptable. Besides the gain of optimization to capture high-frequency phenomena is also underlined. Adding order constraints to the optimization allows an interesting trade-off when a large range of scales is considered. Finally, the ability of the present overset strategy to preserve accuracy is illustrated by the diffraction of an acoustic source by two cylinders, and the generation of acoustic tones in a rotor–stator interaction. Some recommandations are formulated in the closing section

Fourth order transport model on Yin-Yang grid by multi-moment constrained finite volume scheme

AbstractA fourth order transport model is proposed for global computation with the application of multi-moment constrained finite volume (MCV) scheme and Yin-Yang overset grid. Using multi-moment concept, local degrees of freedom (DOFs) are point-wisely defined within each mesh element to build a cubic spatial reconstruction. The updating formulations for local DOFs are derived by adopting multi moments as constraint conditions, including volume-integrated average (VIA), point value (PV) and first order derivative value (DV). Using Yin-Yang grid eliminates the polar singularities and results in a quasi-uniform mesh over the whole globe. Each component of Yin-Yang grid is a part of the LAT-LON grid, an orthogonal structured grid, where the MCV formulations designed for Cartesian grid can be applied straightforwardly to develop the high order numerical schemes. Proposed MCV model is checked by widely used benchmark tests. The numerical results show that the present model has fourth order accuracy and is competitive to most existing ones

Deformable Overset Grid for Multibody Unsteady Flow Simulation

A deformable overset grid method is proposed to simulate the unsteady aerodynamic problems with multiple flexible moving bodies. This method uses an unstructured overset grid coupled with local mesh deformation to achieve both robustness and efficiency. The overset grid hierarchically organizes the subgrids into clusters and layers, allowing for overlapping/embedding of different type meshes, in which the mesh quality and resolution can be independently controlled. At each time step, mesh deformation is locally applied to the subgrids associated with deforming bodies by an improved Delaunay graph mapping method that uses a very coarse Delaunay mesh as the background graph. The graph is moved and deformed by the spring analogy method according to the specified motion, and then the computational meshes are relocated by a simple one-to-one mapping. An efficient implicit hole-cutting and intergrid boundary definition procedure is implemented fully automatically for both cell-centered and cell-vertex schemes based on the wall distance and an alternative digital tree data search algorithm. This method is successfully applied to several complex multibody unsteady aerodynamic simulations, and the results demonstrate the robustness and efficiency of the proposed method for complex unsteady flow problems, particularly for those involving simultaneous large relative motion and self-deformation

Tiltrotor CFD part I: validation

This paper presents performance analyses of the model-scale ERICA and TILTAERO tiltrotors and of the full-scale XV-15 rotor with high-fidelity computational fluids dynamics. For the ERICA tiltrotor, the overall effect of the blades on the fuselage was well captured, as demonstrated by analysing surface pressure measurements. However, there was no available experimental data for the blade aerodynamic loads. A comparison of computed rotor loads with experiments was instead possible for the XV-15 rotor, where CFD results predicted the FoM within 1.05%. The method was also able to capture the differences in performance between hover and propeller modes. Good agreement was also found for the TILTAERO loads. The overall agreement with the experimental data and theory for the considered cases demonstrates the capability of the present CFD method to accurately predict tiltrotor flows. In a second part of this work, the validated method is used for blade shape optimisation