David Zingg

University of Toronto | U of T · Institute for Aerospace Studies

We present a new class of efficient and robust discontinuous spectral-element methods of arbitrary order for nonlinear hyperbolic systems of conservation laws on curved triangular and tetrahedral unstructured grids. Such discretizations employ a recently introduced family of sparse tensor-product summation-by-parts (SBP) operators in collapsed coor...

Conventional tube-and-wing and proposed blended-wing-body airliners must satisfy several design requirements, but the latter configuration is tightly integrated and sensitive to these requirements. In this work, blended-wing-body regional aircraft are investigated using a gradient-based mixed-fidelity multidisciplinary optimization framework center...

Multidimensional diagonal-norm summation-by-parts (SBP) operators with collocated volume and facet nodes, known as diagonal-E\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{docume...

We present novel fully-symmetric quadrature rules with positive weights and strictly interior nodes of degrees up to 84 on triangles and 40 on tetrahedra. Initial guesses for solving the nonlinear systems of equations needed to derive quadrature rules are generated by forming tensor-product structures on quadrilateral/hexahedral subdomains of the s...

We present an approach to construct efficient sparse summation-by-parts (SBP) operators on triangles and tetrahedra with a tensor-product structure. The operators are constructed by splitting the simplices into quadrilateral or hexahedral subdomains, mapping tensor-product SBP operators onto the subdomains, and assembling back using a continuous-Ga...

We present an extension of the summation-by-parts (SBP) framework to tensor-product spectral-element operators in collapsed coordinates. The proposed approach enables the construction of provably stable discretizations of arbitrary order which combine the geometric flexibility of unstructured triangular and tetrahedral meshes with the efficiency of...

Gaussian processes provide probabilistic surrogates for various applications including classification, uncertainty quantification, and optimization. Using a gradient‐enhanced covariance matrix can be beneficial since it provides a more accurate surrogate relative to its gradient‐free counterpart. An acute problem for Gaussian processes, particularl...

High-fidelity aerodynamic optimization based on the Reynolds-averaged Navier-Stokes equations is used to investigate the aerodynamic performance of the Flying V aircraft configuration. The Flying V aircraft’s performance is assessed in the wide-body and single-aisle classes, sized to match the capabilities of the Airbus A350-900 and A320neo, respec...

We present a new class of efficient and robust discontinuous spectral-element methods of arbitrary order for nonlinear hyperbolic systems of conservation laws on curved triangular and tetrahedral unstructured grids. Such discretizations employ a recently introduced family of sparse tensor-product summation-by-parts (SBP) operators in collapsed coor...

Multidimensional diagonal-norm summation-by-parts (SBP) operators with collocated volume and facet nodes, known as diagonal-E operators, are attractive for entropy-stable discretizations from an efficiency standpoint. However, there is a limited number of such operators, and those currently in existence often have a relatively high node count for a...

A new formula is derived for the random error of sample central moments from correlated data which does not assume an underlying distribution and is accurate to leading order in the number of sample elements. Central moments, being important quantities in turbulence research, require accurate error estimation. Many approaches have been followed in...

Gaussian processes provide probabilistic surrogates for various applications including classification, uncertainty quantification, and optimization. Using a gradient-enhanced covariance matrix can be beneficial since it provides a more accurate surrogate relative to its gradient-free counterpart. An acute problem for Gaussian processes, particularl...

We present an extension of the summation-by-parts (SBP) framework to tensor-product spectral-element operators in collapsed coordinates. The proposed approach enables the construction of provably stable discretizations of arbitrary order which combine the geometric flexibility of unstructured triangular and tetrahedral meshes with the efficiency of...

High-order Hadamard-form entropy stable multidimensional summation-by-parts discretizations of the Euler and Navier-Stokes equations are considerably more expensive than the standard divergence-form discretization. In search of a more efficient entropy stable scheme, we extend the entropy-split method for implementation on unstructured grids and in...

This paper presents an assessment of the potential fuel burn savings offered by the transonic strut-braced-wing configuration within the single-aisle class of aircraft relative to a modern conventional tube-and-wing through aerodynamic shape optimization based on the Reynolds-averaged Navier-Stokes equations. A representative strut-braced-wing airc...

Gaussian processes (GPs) are used for numerous different applications, including uncertainty quantification and optimization. Ill-conditioning of the covariance matrix for GPs is common with the use of various kernels, including the Gaussian, rational quadratic, and Matérn kernels. A common approach to overcome this problem is to add a nugget along...

In aerodynamic shape optimization, traditional static geometry control methods can produce suboptimal performance by introducing performance tradeoffs at various stages of optimization, enforcing arbitrary constraints on open-ended optimization, and necessitating foreknowledge of problem behavior to design an effective control scheme. These shortco...

This paper presents an exploration of the aerodynamic design of a box-wing aircraft concept through high-fidelity aerodynamic shape optimization. The optimization framework consists of B-spline parameterization surfaces, an integrated mesh parameterization and deformation scheme based on the theory of linear elasticity , free-form and axial deforma...

This paper presents progress toward a transition modelling capability for use in the numerical solution of the Reynolds-averaged Navier-Stokes equations that provides accurate predictions for transonic flows and is thus suitable for use in the design of wings for aircraft flying at transonic speeds. To this end, compressibility corrections are deve...

The goal of this paper is to outline the requirements for obtaining accurate solutions and functionals from high-order tensor-product generalized summation-by-parts discretizations of the steady two-dimensional linear convection and Euler equations on general curved domains. Two procedures for constructing high-order grids using either Lagrange or...

Unconventional aircraft configurations promise large improvements in energy efficiency over the current conventional tube-and-wing configuration, but their industrial adoption is impeded by significant design challenges and the associated financial and technological risks. Recent advances in optimization frameworks, including the integration of hig...

In one dimension, nodal locations that are distinct are necessary and sufficient to ensure that a unique polynomial interpolant exists for data provided at a set of nodes, i.e. that the set of nodes is unisolvent. In multiple dimensions however, unisolvency for a polynomial interpolant of degree p is not ensured even with nodal locations that are d...

We propose a unifying framework for the matrix-based formulation and analysis of discontinuous Galerkin (DG) and flux reconstruction (FR) methods for conservation laws on general unstructured grids. Within such an algebraic framework, the multidimensional summation-by-parts (SBP) property is used to establish the discrete equivalence of strong and...

We present provably stable and conservative discretizations of arbitrary order which exploit the geometric flexibility afforded by triangular elements alongside the computational efficiency of tensor-product operators through the use of a collapsed coordinate transformation. Collocated nodal approximations as well as modal formulations employing or...

Results are presented that summarize how to obtain accurate functionals from dual-consistent generalized summation-by-parts discretizations when solving problems of increasing practical complexity. These results include showing that an optimized approach for approximating grid metrics is important for obtaining accurate functionals with Legendre-Ga...

This paper presents a relative fuel burn evaluation of the transonic strut-braced-wing configuration for the regional aircraft class in comparison to an equivalent conventional tube-and-wing aircraft. This is accomplished through multipoint aerodynamic shape optimisation based on the Reynolds-averaged Navier-Stokes equations. Aircraft concepts are...

The ability to morph the shape of an aircraft wing to optimize performance is widely accepted as a path to improved aircraft efficiency. A simpler approach is to change the wing camber using existing control surfaces. In this work, a Reynolds-averaged Navier–Stokes-based aerodynamic shape optimization methodology is applied to the design of a busin...

In recent decades, the environmental impacts of aviation have become a key challenge for the aeronautical community. Advanced and well-established technologies such as active flow control systems, wing-tip devices, high bypass ratio engines, composite materials, among others, have demonstrated fuel-burn benefits by reducing drag and/or weight. Neve...

A high-fidelity aerodynamic shape optimization framework based on the Reynolds-averaged Navier–Stokes equations is applied to the optimization of a boundary-layer ingesting S-duct designed for embedded engines on a high-subsonic, unmanned flight vehicle. The optimizations initially target a cruise operating condition and are further extended to sin...

This paper presents a methodology for dynamic aeroelastic analysis of aircraft based on model order reduction with error estimation. A projection-based model order reduction approach is used to create an aerodynamic reduced-order model (ROM) which is coupled to a structural model to create an aeroelastic ROM. The governing aerodynamic equations are...

A smooth local correlation-based transition model is fully coupled to a RANS-based Newton-Krylov flow solver and discrete-adjoint gradient-based optimization algorithm. The free-transition optimization framework is evaluated using lift-constrained drag minimizations of airfoils at design conditions ranging from light to single-aisle aircraft and an...

The numerical behaviour of transport-equation-based transition models, including both iterative and grid convergence, is influenced by the source terms. Transition models contain source terms that are large and highly nonlinear, and can be destabilizing in a strong implicit solver. Linearization strategies with varying levels of coupling are evalua...

We analyze the stability and functional superconvergence of discretizations of diffusion problems with the narrow-stencil second-derivative generalized summation-by-parts (SBP) operators coupled with simultaneous approximation terms (SATs). Provided that the primal and adjoint solutions are sufficiently smooth and the SBP-SAT discretization is prim...

The aerodynamic design and fuel burn performance of a Mach-0.78 strut-braced-wing regional jet is investigated through aerodynamic shape optimization based on the Reynolds-averaged Navier–Stokes equations. Conceptual-level multidisciplinary design optimization is first performed to size the strut-braced-wing aircraft for a design mission similar to...

View Video Presentation: https://doi.org/10.2514/6.2021-2468.vid A high-fidelity aerodynamic shape optimization framework based on the Reynolds-Averaged Navier-Stokes equations is applied to the optimization of a boundary layer ingesting S-duct designed for embedded engines on a high-subsonic, unmanned flight vehicle. The optimizations initially ta...

View Video Presentation: https://doi.org/10.2514/6.2021-3031.vid This work presents novel progressive and adaptive dynamic geometry control algorithms which seek to improve convergence and reduce user workload by partially automating the design of effective geometry control systems for aerodynamic shape optimization. These algorithms function by be...

View Video Presentation: https://doi.org/10.2514/6.2021-3028.vid An aerodynamic shape optimization framework for unsteady flow is applied to a range of two- and three-dimensional laminar flows. The shape optimization framework uses free-form deformation for geometry control with an underlying B-spline surface parameterization integrated with an eff...

View Video Presentation: https://doi.org/10.2514/6.2021-2547.vid This paper presents a methodology for dynamic aeroelastic analysis of aircraft based on model order reduction with error estimation. A projection-based model order reduction approach is used to create an aerodynamic reduced-order model (ROM) which is coupled to a structural model to c...

Several types of simultaneous approximation term (SAT) for diffusion problems discretized with diagonal-norm multidimensional summation-by-parts (SBP) operators are analyzed based on a common framework. Conditions under which the SBP-SAT discretizations are consistent, conservative, adjoint consistent, and energy stable are presented. For SATs lead...

The aerodynamic design and fuel burn performance of a Mach 0.78 strut-braced-wing regional jet is investigated through aerodynamic shape optimization based on the Reynolds-averaged Navier-Stokes equations. Conceptual-level multidisciplinary design optimization is first performed to size the strut-braced-wing aircraft for a design mission similar to...

We propose a unifying framework for the matrix-based formulation and analysis of discontinuous Galerkin (DG) and flux reconstruction (FR) methods for conservation laws on general unstructured grids. Within such an algebraic framework, the multidimensional summation-by-parts (SBP) property is used to establish the discrete equivalence of strong and...

Typical aerodynamic shape optimization and multidisciplinary optimization algorithms omit high-fidelity flutter predictions due to the associated computational costs. This paper presents a model order reduction framework as a step toward flutter-constrained aircraft optimization. The Euler equations linearized about a steady-state solution of the n...

We analyze the stability and functional superconvergence of discretizations of diffusion problems with the narrow-stencil second-derivative generalized summation-by-parts (SBP) operators coupled with simultaneous approximation terms (SATs). Provided that the primal and adjoint solutions are sufficiently smooth and the SBP-SAT discretization is prim...

Regional-class hybrid wing-body (HWB) aircraft that satisfy various stability and control requirements are optimized for a combination of cruise drag and maximum takeoff weight by using a multifidelity multidisciplinary optimization framework based on solutions to the Reynolds-averaged Navier-Stokes equations. The design mission consists of flying...

Several types of simultaneous approximation term (SAT) for diffusion problems discretized with diagonal-norm multidimensional summation-by-parts (SBP) operators are analyzed based on a common framework. Conditions under which the SBP-SAT discretizations are consistent, conservative, adjoint consistent, and energy stable are presented. For SATs lead...

A gradient-based multistart method based on a set of 17 to 33 random initial geometries is used to examine the risk associated with multimodality when applying gradient-based optimization to aerodynamic shape optimization. Aerodynamic shape optimization problems typical of detailed, preliminary, and exploratory design are shown to consistently pres...

A smooth version of the γ-Reθt local correlation-based transition model (LM2015) for the Spalart–Allmaras (SA) turbulence model is presented. The LM2015 model with helicity-based crossflow correlations is modified and coupled to the SA turbulence model, designated SA-LM2015. The LM2015 and SA-LM2015 transition models include source terms that conta...

We develop high-order entropy-conservative semi-discrete schemes for hyperbolic conservation laws applicable to non-conforming curvilinear grids arising from h-, p-, or hp-adaptivity. More precisely, building on previous work with conforming grids by Crean et al. (Journal of Computational Physics, vol. 356, pp. 410-438, Mar. 2018) and Chan et al. (...

This paper presents the cross validation of two aerodynamic shape optimization methodologies in order to validate, characterize, and compare the two methodologies. Both methodologies use gradient-based optimization based on the Reynolds-averaged Navier–Stokes equations driven by the discrete adjoint method. The first methodology uses a B-spline sur...

We investigate superconvergent functional estimates in curvilinear coordinates for diagonal-norm tensor-product generalized summation-by-parts operators. We show that interpolation/extrapolation operators of degree greater than or equal to 2p are required to preserve at least 2p quadrature accuracy and functional superconvergence in curvilinear coo...

Typical aerodynamic shape and multidisciplinary optimization algorithms omit high-fidelity flutter predictions due to the associated computational costs. This paper presents a model order reduction framework as a step towards flutter constrained aircraft optimization. The Euler equations linearized about a steady-state solution are used as the gove...

Methodologies are presented that enable the construction of provably linearly stable and conservative high-order discretizations of partial differential equations in curvilinear coordinates based on generalized summation-by-parts operators, including operators with dense-norm matrices. Specifically, three approaches are presented for the constructi...

A fully-coupled, implicit Newton-Krylov algorithm with laminar-turbulent boundary-layer transition prediction capabilities for three-dimensional external aerodynamic flows has been developed. The γ-Reθt Local Correlation-Based Transition Model with helicity-based crossflow correlations is modified and fully coupled to the Spalart-Allmaras turbulenc...

Methods of satisfying the stability and control (S&C) requirements for hybrid wing–body (HWB) aircraft are investigated using a multifidelity multidisciplinary optimization framework. A Reynolds-averaged Navier–Stokes solver is used for aerodynamic prediction, together with conceptual-level weight and balance models. These are coupled with a gradie...

A matrix-free monolithic homotopy continuation algorithm is developed which allows for approximate numerical solutions to nonlinear systems of equations without the need to solve a linear system, thereby avoiding the formation of any Jacobian or preconditioner matrices. The algorithm can converge from an arbitrary starting guess, under suitable con...

Cambridge Core - Environmental Law - Sustainable Development, International Aviation, and Treaty Implementation - edited by Armand L.C. de Mestral

Sustainable Development, International Aviation, and Treaty Implementation - edited by Armand L.C. de Mestral September 2018

The predictor component of a monolithic homotopy continuation algorithm is augmented with higher derivative information for use as an efficient, robust, and scalable continuation algorithm suitable for application to large sparse systems of nonlinear algebraic equations. Convergence of the algorithm is established analytically, and efficiency studi...

The summation-by-parts (SBP) property can be used to construct high-order provably stable numerical methods. A general framework is explored for deriving provably stable and conservative artificial dissipation operators for use with high-order traditional and element-type SBP operators on general nodal distributions, thus enabling the time stable a...

Non-conforming numerical approximations offer increased flexibility for applications that require high resolution in a localized area of the computational domain or near complex geometries. Two key properties for non-conforming methods to be applicable to real world applications are conservation and energy stability. The summation-by-parts (SBP) pr...

This paper is concerned with the accurate, conservative, and stable imposition of boundary conditions and inter-element coupling for multi-dimensional summation-by-parts (SBP) finite-difference operators. More precisely, the focus is on diagonal-norm SBP operators that are not based on tensor products and are applicable to unstructured grids compos...

The Applied Aerodynamics Technical Committee of AIAA launched an optimization discussion group, the Aerodynamic Design Optimization Discussion Group, in 2013. One of the four benchmark test cases is based on the NACA 0012 airfoil and solutions of the Euler equations with prescribed objective function and geometric constaints. Volunteer participants...

Through aerostructural optimization, this paper presents progress toward characterizing the potential efficiency gains of drooped wings for commercial aircraft in transonic flight. The drooped wing is a nonplanar configuration with downward spanwise camber from the wing root to the tip. The aerostructural optimization cases include two load conditi...

We present and analyze an entropy-stable semi-discretization of the Euler equations based on high-order summation-by-parts (SBP) operators. In particular, we consider general multidimensional SBP elements, building on and generalizing previous work with tensor–product discretizations. In the absence of dissipation, we prove that the semi-discrete s...

An efficient and robust solution algorithm for the aerostructural analysis and coupled adjoint problems is crucial to the success of high-fidelity aerostructural optimization. The objective of the present paper is to investigate ways to maximize the efficiency of a monolithic solution method and further quantify its benefits in the context of aeros...