摘要 :
We present mesh node movement as an effective discretization error control strategy for shape optimization problems on structured meshes. The context is aerodynamic shape optimization via mesh deformation on anisotropic, structure...
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We present mesh node movement as an effective discretization error control strategy for shape optimization problems on structured meshes. The context is aerodynamic shape optimization via mesh deformation on anisotropic, structured meshes suitable for Reynolds-averaged Navier-Stokes (RANS) simulations. Movement of interior nodes occurs concurrently with the shape optimization iterations, with the objective of minimizing the output error for a fixed mesh size. The output-based error estimates that drive the node movement rely on an adjoint solution that is also used by the gradient-based shape optimization. In the context of high-order solution approximation on curved meshes, the high-order mesh nodes provide additional degrees of freedom for controlling the discretization error. Even though many of the meshes of interest are structured, a metric-based mesh optimization algorithm is used in an intermediate step to provide element sizing and anisotropy information. The objective of the node movement is then to make the mesh better conform to the computed metric field. Results from two-dimensional aerodynamics shape optimization problems demonstrate the ability of the node movement to decrease discretization error, and the efficacy of the output error estimates.
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摘要 :
We present mesh node movement as an effective discretization error control strategy for shape optimization problems on structured meshes. The context is aerodynamic shape optimization via mesh deformation on anisotropic, structure...
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We present mesh node movement as an effective discretization error control strategy for shape optimization problems on structured meshes. The context is aerodynamic shape optimization via mesh deformation on anisotropic, structured meshes suitable for Reynolds-averaged Navier-Stokes (RANS) simulations. Movement of interior nodes occurs concurrently with the shape optimization iterations, with the objective of minimizing the output error for a fixed mesh size. The output-based error estimates that drive the node movement rely on an adjoint solution that is also used by the gradient-based shape optimization. In the context of high-order solution approximation on curved meshes, the high-order mesh nodes provide additional degrees of freedom for controlling the discretization error. Even though many of the meshes of interest are structured, a metric-based mesh optimization algorithm is used in an intermediate step to provide element sizing and anisotropy information. The objective of the node movement is then to make the mesh better conform to the computed metric field. Results from two-dimensional aerodynamics shape optimization problems demonstrate the ability of the node movement to decrease discretization error, and the efficacy of the output error estimates.
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This paper presents a method for gradient-based shape optimization using unsteady models of turbulent flowfields, for which forward simulations are already expensive and adjoint calculations diverge or require costly regularizatio...
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This paper presents a method for gradient-based shape optimization using unsteady models of turbulent flowfields, for which forward simulations are already expensive and adjoint calculations diverge or require costly regularization. The proposed method targets an objective and constraints computed from the time-averaged flowfield and does not store the forward time history or compute an unsteady adjoint. It instead relies on the field-inversion, machine-learning (FIML) approach, in which a correction field modifies the production term in a Reynolds-averaged Navier-Stokes (RANS) model of the flow. Steady, adjoint-based, field inversion yields this correction field, and a neural-network model is trained to reproduce this field from local flow quantities. Gradient-based shape optimization is performed using the corrected RANS model, which includes a linearization of the correction field calculation for accurate gradients. The complete design optimization loop consists of iterations of unsteady simulation, FIML, and steady optimization. Low and moderate Reynolds number airfoil optimization problems demonstrate the performance of the proposed method, and comparisons to RANS-alone designs illustrate the importance of accounting for the unsteady flow effects in the optimization.
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This paper presents a method for performing output-based mesh adaptation for large-eddy simulations of turbulence. Instead of an unsteady adjoint, which is expensive to compute and requires non-trivial regularization, the method i...
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This paper presents a method for performing output-based mesh adaptation for large-eddy simulations of turbulence. Instead of an unsteady adjoint, which is expensive to compute and requires non-trivial regularization, the method is based on the field-inversion and machine-learning approach to data-driven turbulence modeling. The data here come not from experiments but from statistics computed from unsteady forward simulations. The resulting trained turbulence models yield steady-state solutions that represent the time-averaged unsteady flow-fields. Adjoints computed from these steady-state models yield the sensitivity information required for an adjoint-weighted residual error estimate and adaptive indicator. Each adaptive iteration then only requires one unsteady primal solution with minimal storage: average statistics and fine-space residual information. Combined with unstructured mesh optimization, the method drives unsteady outputs to accurate values in only a few adaptive iterations. The performance is demonstrated on two-dimensional, low Reynolds number airfoil simulations, and comparisons are made to other techniques, including uniform and residual-based adaptation.
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摘要 :
This paper presents a method for performing output-based mesh adaptation for large-eddy simulations of turbulence. Instead of an unsteady adjoint, which is expensive to compute and requires non-trivial regularization, the method i...
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This paper presents a method for performing output-based mesh adaptation for large-eddy simulations of turbulence. Instead of an unsteady adjoint, which is expensive to compute and requires non-trivial regularization, the method is based on the field-inversion and machine-learning approach to data-driven turbulence modeling. The data here come not from experiments but from statistics computed from unsteady forward simulations. The resulting trained turbulence models yield steady-state solutions that represent the time-averaged unsteady flow-fields. Adjoints computed from these steady-state models yield the sensitivity information required for an adjoint-weighted residual error estimate and adaptive indicator. Each adaptive iteration then only requires one unsteady primal solution with minimal storage: average statistics and fine-space residual information. Combined with unstructured mesh optimization, the method drives unsteady outputs to accurate values in only a few adaptive iterations. The performance is demonstrated on two-dimensional, low Reynolds number airfoil simulations, and comparisons are made to other techniques, including uniform and residual-based adaptation.
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This paper presents a study of temporal errors, as well as a time-step control strategy for their reduction, in high-order spatial discretizations of convection-dominated flow equations. The discontinuous Galerkin finite-element m...
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This paper presents a study of temporal errors, as well as a time-step control strategy for their reduction, in high-order spatial discretizations of convection-dominated flow equations. The discontinuous Galerkin finite-element method serves as the spatial discretization, and it is combined with implicit, semi-discrete time-marching schemes. Efficiency of the schemes, measured in terms of the number of implicit system solutions for a given level of accuracy, is compared for different spatial orders and mesh sizes. For uniform time stepping, certain hybrid multi-step/stage schemes can be more efficient than popular diagonally-implicit Runge-Kutta methods. A residual-based adaptive time-step control strategy is also presented for balancing spatial and temporal errors in each time step, with a focus on performance on spatially-adapted meshes. The methods are tested on an unsteady manufactured solution for scalar advection-diffusion, and for the Navier-Stokes equations on two problems with moving geometry and mesh.
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One technique for capturing shocks with high-order methods is through artificial viscosity. Key considerations of this approach are (1) deciding the amount of artificial viscosity to add; (2) maintaining stability and efficiency o...
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One technique for capturing shocks with high-order methods is through artificial viscosity. Key considerations of this approach are (1) deciding the amount of artificial viscosity to add; (2) maintaining stability and efficiency of the nonlinear solver; and (3) ensuring the accuracy of the resulting solutions, particularly in the presence of strong shocks. To address (1), we compare a switch based on intra-element solution variation with one based on the difference between the solution and its low-order projection. To address point (2), we forego a complete linearization of the artificial viscosity contribution to the residual, in order to keep the residual Jacobian stencil compact. To address (3), we introduce the viscosity in a piecewise-continuous fashion to avoid spurious entropy production. Furthermore, we use output-based error estimation and mesh optimization to minimize the output error. We test the method on aerodynamic flow applications ranging from transonic to supersonic, discretized using standard discontinuous Galerkin (DG) and hybridized DG.
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This paper presents a stability and performance analysis of iterative solution methods for hybridized discontinuous Galerkin (HDG) discretizations. These discretizations reduce the number of globally-coupled unknowns in an implici...
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This paper presents a stability and performance analysis of iterative solution methods for hybridized discontinuous Galerkin (HDG) discretizations. These discretizations reduce the number of globally-coupled unknowns in an implicit solver through a static condensation procedure, resulting in a scaling of the unknowns that is one power lower than in standard discontinuous Galerkin (DG). Embedded discontinuous Galerkin (EDG) methods offer the largest such reduction by restricting the trace approximation space to be continuous at edges and nodes. However, the reduction of unknowns in HDG and EDG comes at the expense of extra processing before and after the global system solution, which can add non-trivial cost to the solution process. In addition, the Schur-complement system exhibits a different structure and iterative solution characteristics compared to the standard DG discretization. Both of these are analyzed in this paper, in the context of convection-dominated flows for aerospace applications. Through analysis and demonstration problems, we show that the favorable stability properties of standard iterative solvers, such as block-Jacobi smoothing, observed in DG do not extend to HDG and EDG. We then suggest variations of some of these smoothers that improve the stability and performance, both stand-alone and in the context of p-multigrid and GMRES. Finally, we show that in spite of the lack of block iterative stability, EDG still shows very good performance for a more powerful solver, GMRES with an incomplete lower-upper (ILU) preconditioner.
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This paper presents a two-step method for performing output-based mesh adaptation using node movement, for high-order discretizations. In the first step, an optimal target metric is determined over the current mesh using an optimi...
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This paper presents a two-step method for performing output-based mesh adaptation using node movement, for high-order discretizations. In the first step, an optimal target metric is determined over the current mesh using an optimization procedure that equidistributes a marginal output error to degree-of-freedom cost. In the second step, the nodes are moved so as to minimize the error between the mesh-implied metric and the target metric, i.e. to make the mesh better conform to the target metric. This movement is the solution of a global optimization problem, made possible by virtue of the meshes being coarse for high-order methods. No additional flow solutions or error calculations take place during this second optimization step, and hence the optimization is not computationally expensive. Results for three diverse cases demonstrate the ability of the mode movement strategy to reduce the output error relative to a given initial mesh, at a level that in one case surpasses that of a baseline re-meshing strategy.
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摘要 :
This paper presents a two-step method for performing output-based mesh adaptation using node movement, for high-order discretizations. In the first step, an optimal target metric is determined over the current mesh using an optimi...
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This paper presents a two-step method for performing output-based mesh adaptation using node movement, for high-order discretizations. In the first step, an optimal target metric is determined over the current mesh using an optimization procedure that equidistributes a marginal output error to degree-of-freedom cost. In the second step, the nodes are moved so as to minimize the error between the mesh-implied metric and the target metric, i.e. to make the mesh better conform to the target metric. This movement is the solution of a global optimization problem, made possible by virtue of the meshes being coarse for high-order methods. No additional flow solutions or error calculations take place during this second optimization step, and hence the optimization is not computationally expensive. Results for three diverse cases demonstrate the ability of the mode movement strategy to reduce the output error relative to a given initial mesh, at a level that in one case surpasses that of a baseline re-meshing strategy.
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