Optimizing High-Order Tet Meshes for Smoothed Particle Hydrodynamics With The Target Matrix Optimization Paradigm
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Computer science↗
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Results for “mesh optimization”
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hr-Adaptivity for nonconforming high-order meshes with the target matrix optimization paradigm
In this study, we present an \(hr\) -adaptivity framework for optimization of high-order meshes. This work extends the r -adaptivity method by Dobrev et al. (Comput Fluids, 2020), where we utilized the Target-Matrix Optimization Paradigm (TMOP) to minimize a functional that depends on each element’s current and target geometric parameters: element aspect-ratio , size , skew , and rotation . Since fixed mesh topology limits the ability to achieve the target size and aspect-ratio at each position, in this paper, we augment the r -adaptivity framework with nonconforming adaptive mesh refinement to further reduce the error with respect to the target geometric parameters. The proposed formulation, referred to as \(hr\) -adaptivity, introduces TMOP-based quality estimators to satisfy the aspect-ratio target via anisotropic refinements and size target via isotropic refinements in each element of the mesh. The methodology presented is purely algebraic, extends to both simplices and hexahedra/quadrilaterals of any order, and supports nonconforming isotropic and anisotropic refinements in 2D and 3D. Using a problem with a known exact solution, we demonstrate the effectiveness of \(hr\) -adaptivity over both r - and \(h\) -adaptivity in obtaining similar accuracy in the solution with significantly fewer mesh nodes. We also present several examples that show that \(hr\) -adaptivity can help satisfy geometric targets even when \(r\) -adaptivity fails to do so, due to the topology of the initial mesh.
42 ENGINEERING↗
Adjoint-Based Mesh Adaptation and Shape Optimization for Simulations with Propulsion
We demonstrate a well-posed formulation of permeable boundary conditions and mass- flow-rate functionals for adjoint-based mesh refinement and shape optimization governed by the steady Euler equations. The boundary conditions are used to model propulsion- system effects of inlets and nozzles. A two-shock diffuser with an analytic solution is used to verify the implementation. Numerical examples show that the adjoint solution is smooth at the boundary, indicating that the discretization is adjoint consistent when exit pressure is specified at subsonic outflow, and stagnation temperature and pressure at subsonic inflow. The results focus on improving simulation techniques for low-boom aircraft analysis and design. By including mass-flow-rate outputs, we obtain reliable estimates of engine flow rates concurrently with nearfield pressure signatures without increasing simulation cost. We also demonstrate the importance of mass-flow-rate constraints in shape optimization by examining trade-offs between maximizing performance of a shrouded supersonic nozzle and minimizing shocks in its nearfield.
Nemec, Marian↗
Level-set topology optimization with PDE generated conformal meshes
This paper presents a level-set topology optimization approach that uses conformal meshes for the analysis of the displacement field. The structure’s boundary is represented by the iso-contour of a level-set field discretized on a fixed background design mesh. The conformal mesh is updated for each design iteration via a PDE based mesh morphing process that identifies the set of facets in the background mesh that are homeomorphic to the boundary and relaxes the homeomorphic mesh to conform to the structure’s boundary and ensure high element quality. The conformal mesh allows for a more accurate computation of the response versus density and some level-set based methods which interpolate material properties using the volume fraction. Numerical examples illustrate the proposed approach by optimizing linear-elastic two- and three-dimensional structures, wherein insight into the performance of the mesh morphing process is provided. The examples also highlight the scalability of the approach.
42 ENGINEERING↗
Advancing the STS Neutron Moderator Design with an Automated Optimization Workflow and Unstructured Mesh Modeling
With the Second Target Station approaching its final design phase, a detailed neutronics evaluation of its critical components is necessary. Optimizing the dimensions of the two cold-source moderators that are at the heart of this facility presents a multi-objective optimization problem for which an accurate geometric description is crucial. We have applied a fully automated optimization workflow in which a detailed unstructured mesh geometry is automatically generated with Attila4MC, starting from a parametrized CREO geometry followed by preprocessing with SpaceClaim. With this geometry, a MCNP run is performed to calculate the brightness metrics, which are subsequently provided to the optimization algorithm in DAKOTA that provides new parameters and drives the optimization loop until convergence. In this paper, we show the results of the analysis that are used for the final design of the cylindrical and tube moderator. The optimization simulations provide a refinement to and confirmation of the conclusions of the previous design iteration. Additional to the optimization, a sensitivity study is performed to study the effect of minor geometry changes, which is important for the final engineering design. In conclusion, with these studies, we demonstrate that the automated workflow and high-fidelity unstructured mesh modeling are efficient tools for a thorough design evaluation.
DAKOTA↗
Mesh independency in topology optimization
The topology optimization community has regularly employed optimization algorithms from the operations research community. However, these algorithms are implemented in the sequence space l2 instead of the proper function space where the design variable resides. In this software, we benchmark the mesh independent implementation of pyMMAopt with three common problems in topology optimization. We show how the volume fraction variable discretization on non-uniform meshes affects the convergence of l2 based optimization algorithms and how pyMMAopt successfully achieves mesh independent convergence.
Salazar De Troya, Miguel↗
A mesh gradient technique for numerical optimization
A class of successive-improvement optimization methods in which directions of descent are defined in the state space along each trial trajectory are considered. The given problem is first decomposed into two discrete levels by imposing mesh points. Level 1 consists of running optimal subarcs between each successive pair of mesh points. For normal systems, these optimal two-point boundary value problems can be solved by following a routine prescription if the mesh spacing is sufficiently close. A spacing criterion is given. Under appropriate conditions, the criterion value depends only on the coordinates of the mesh points, and its gradient with respect to those coordinates may be defined by interpreting the adjoint variables as partial derivatives of the criterion value function. In level 2, the gradient data is used to generate improvement steps or search directions in the state space which satisfy the boundary values and constraints of the given problem.
Willis, E. A., Jr.↗
Adjoint-Based Mesh Adaptation and Shape Optimization for Simulations with Propulsion
Objectives: Reliable evaluation of mass flow rates through permeable boundaries - Estimate and control discretization error- Consider both computational domain outflow and inflow- Applicable to simulating propulsion-system effects, as well as secondary flow paths - Explore feasibility of handling more general outputs at domain boundaries. Design optimization subject to mass-flow-rate constraints - Improve aerodynamic performance and reduce noise due to sonic boom - Control discretization error in design space to improve confidence in final designs.
Nemec, Marian↗
Variable-fidelity multipoint aerodynamic shape optimization with output-based adapted meshes
This work presents a method to control the discretization error in multipoint aerodynamic shape optimization using output-based adapted meshes. The meshes are adapted via adjoint-based error estimates, taking into account both the objective and constraint output errors. A multi-fidelity optimization framework is then developed by taking advantage of the variable fidelity offered by adaptive meshes. The objective functional and its sensitivity at each design point (operating condition) are first evaluated on the same initial coarse mesh, which is then subsequently adapted for each design point individually as the shape optimization proceeds. The effort to set up the optimization is minimal since the initial mesh can be fairly coarse and easy to generate. As the shape approaches the optimal design, the mesh at each design point becomes finer, in regions necessary for that particular operating condition. The multi-fidelity framework is tightly coupled with the objective error estimation to ensure the optimization accuracy at each fidelity. Computational savings arise from a reduction of the mesh size when the design is far from optimal and avoiding an exhaustive search on low-fidelity meshes. The proposed method is demonstrated on multipoint drag minimization problems of a transonic airfoil with lift and area constraints. Improved accuracy and efficiency are shown compared to traditional fixed-fidelity optimization with a fixed computational mesh.
42 ENGINEERING↗
Coordination of Behind-the-Meter Energy Storage and Building Loads: Optimization with Deep Learning Models*
With the increasing penetration of renewable energy systems and energy storage systems in buildings, it is critical to optimize system operation. In this paper, we develop an optimization strategy to minimize the operation cost as well as maintain indoor thermal comfort, for a building integrated with battery and PV. A Recurrent Neural Network (RNN) is used to predict building thermal load and zone temperatures. A black-box optimization algorithm known as nonlinear optimization by mesh adaptive direct search (NOMADS) is employed in simulation to provide look-ahead optimal battery dispatch and zone temperature set-point schedules so that the operation cost is minimized. Field data collected from a medium sized office building at Pacific Northwest National Laboratory (PNNL) integrated with Photovoltaic (PV) system model and battery storage system model is used to demonstrate the proposed methodology. Compared with rule based methods, the optimization strategy obtained a lower cost of operation while satisfying comfort constraints.
Chen, Yimin↗
A dual mesh method with adaptivity for stress-constrained topology optimization
This paper is concerned with the topological optimization of elastic structures, with the goal of minimizing the compliance and/or mass of the structure, subject to a stress constraint. It is well known that depending upon the geometry and the loading conditions, the stress field can exhibit singularities, if these singularities are not adequately resolved, the topological optimization process will be ineffective. For computational efficiency, adaptive mesh refinement is required to adequately resolve the stress field. This poses a challenge for the traditional Solid Isotropic Material with Penalization (SIMP) method that employs a one-to-one correspondence between the finite element mesh and the optimization design variables because as the mesh is refined, the optimization process must somehow be re-started with a new set of design variables. The proposed solution here is a dual mesh approach, one finite element mesh defines the material distribution, a second finite element mesh is used for the computation of the displacement and stress fields. This allows for stress-based adaptive mesh refinement without modifying the definition of the optimization design variables. A second benefit of this dual mesh approach is that there is no need to apply a filter to the design variables to enforce a length scale, instead the length scale is determined by the design mesh. This reduces the number of design variables and allows the designer to apply spatially varying length scale if desired. The efficacy of this dual mesh approach is established via several stress-constrained topology optimization problems.
36 MATERIALS SCIENCE↗
Fixed-target serial crystallography at the Structural Biology Center
Serial synchrotron crystallography enables the study of protein structures under physiological temperature and reduced radiation damage by collection of data from thousands of crystals. The Structural Biology Center at Sector 19 of the Advanced Photon Source has implemented a fixed-target approach with a new 3D-printed mesh-holder optimized for sample handling. The holder immobilizes a crystal suspension or droplet emulsion on a nylon mesh, trapping and sealing a near-monolayer of crystals in its mother liquor between two thin Mylar films. Data can be rapidly collected in scan mode and analyzed in near real-time using piezoelectric linear stages assembled in an XYZ arrangement, controlled with a graphical user interface and analyzed using a high-performance computing pipeline. Here, the system was applied to two β-lactamases: a class D serine β-lactamase from Chitinophaga pinensis DSM 2588 and L1 metallo-β-lactamase from Stenotrophomonas maltophilia K279a.
59 BASIC BIOLOGICAL SCIENCES↗
802.11s Wireless Mesh Network Visualization Application
Results of past experimentation at NASA Johnson Space Center showed that the IEEE 802.11s standard has better performance than the widely implemented alternative protocol B.A.T.M.A.N (Better Approach to Mobile Ad hoc Networking). 802.11s is now formally incorporated into the Wi- Fi 802.11-2012 standard, which specifies a hybrid wireless mesh networking protocol (HWMP). In order to quickly analyze changes to the routing algorithm and to support optimizing the mesh network behavior for our intended application a visualization tool was developed by modifying and integrating open source tools.
Mauldin, James Alexander↗
Comparing Unstructured Adaptive Mesh Solutions for the High Lift Common Research Model Airfoil
Discretization error is a common source of uncertainty in Computational Fluid Dynamics (CFD) analyses. Traditional means of controlling discretization error through fixed-mesh refinement studies has proven to be difficult particularly when modeling complex geometries and flow fields. One reason for this is that mesh generation in today’s production CFD workflow is often a labor intensive process that is heavily dependent on user judgment. Unstructured mesh adaptation is known to be an efficient way to control discretization errors in CFD. Adaptive methods replace user based decision making with automated processes that optimize a mesh to reduce discretization error. This paper compares the application of multiple solution adaptive techniques in combination with multiple flow solvers to solve for the flow field about a 2D airfoil section of the NASA High-Lift Common Research Model (HL-CRM). By driving the adaptive mesh processes to a similar level of mesh convergence, the ability to achieve consistent results between multiple adaptive techniques and flow solvers is demonstrated. Mesh convergence for the various adaptive mesh approaches is compared identifying potential areas for improvement and providing mesh generation guidance for future workshops.
mesh adaptation high-lift 2D airfoil↗
Comparing Unstructured Adaptive Mesh Solutions for the High Lift Common Research Model Airfoil
Discretization error is a common source of uncertainty in Computational Fluid Dynamics (CFD) analyses. Traditional means of controlling discretization error through fixed-mesh refinement studies has proven to be difficult particularly when modeling complex geometries and flow fields. One reason for this is that mesh generation in today’s production CFD workflow is often a labor intensive process that is heavily dependent on user judgment. Unstructured mesh adaptation is known to be an efficient way to control discretization errors in CFD. Adaptive methods replace user based decision making with automated processes that optimize a mesh to reduce discretization error. This paper compares the application of multiple solution adaptive techniques in combination with multiple flow solvers to solve for the flow field about a 2D airfoil section of the NASA High-Lift Common Research Model (HL-CRM). By driving the adaptive mesh processes to a similar level of mesh convergence, the ability to achieve consistent results between multiple adaptive techniques and flow solvers is demonstrated. Mesh convergence for the various adaptive mesh approaches is compared identifying potential areas for improvement and providing mesh generation guidance for future workshops.
mesh adaptation↗
An Eulerian Vlasov-Fokker–Planck algorithm for spherical implosion simulations of inertial confinement fusion capsules
Here, we present a numerical algorithm that enables a phase-space adaptive Eulerian Vlasov–Fokker–Planck (VFP) simulation of inertial confinement fusion (ICF) capsule implosions. The approach relies on extending a recent mass, momentum, and energy conserving phase-space moving-mesh adaptivity strategy to spherical geometry. In configuration space, we employ a mesh motion partial differential equation (MMPDE) strategy while, in velocity space, the mesh is expanded/contracted and shifted with the plasma’s evolving temperature and drift velocity. The mesh motion is dealt with by transforming the underlying VFP equations into a computational (logical) coordinate, with the resulting inertial terms carefully discretized to ensure conservation. To deal with the spatial and temporally varying dynamics in a spherically imploding system, we have developed a novel nonlinear stabilization strategy for MMPDE in the configuration space. The strategy relies on a nonlinear optimization procedure that optimizes between mesh quality and the volumetric rate change of the mesh to ensure both accuracy and stability of the solution. Implosions of ICF capsules are driven by several boundary conditions: (1) an elastic moving wall boundary; (2) a time-dependent Maxwellian Dirichlet boundary; and (3) a pressure-driven Lagrangian boundary. Of these, the pressure-driven Lagrangian boundary driver is new to our knowledge. The implementation of our strategy is verified through a set of test problems, including the Guderley and Van-Dyke implosion problems — the first-ever reported using a Vlasov–Fokker–Planck model.
1D2V↗
Divertor heat load estimates on NSTX and DIII-D using new and open-source 2D inversion analysis code
A thermography inversion algorithm has been developed in the open-source Python-based computer code, HYPERION, to calculate the heat flux incident on plasma-facing components (PFCs) in axisymmetric tokamaks. The chosen mesh size at the surface significantly affects the calculated transient heat flux results. The calculated transient heat flux will exceed the real value when the mesh size tends to zero but will underestimate the real value when the mesh size is large. A criterion for determining the appropriate mesh size for the transient heat flux calculation will be discussed. The numerical scheme for HYPERION uses a 2D fully implicit finite-difference approach, allowing temperature-dependent thermal properties of PFC materials. The inversion algorithm is benchmarked against established heat flux calculation codes, TACO and THEODOR, based on thermography data from NSTX and DIII-D respectively. The primary benefits of HYPERION compared to TACO and THEODOR are that it is open-source and it allows for the optimization of mesh thickness along the substrate. The algorithm also accounts for the thermal properties of thin surface layers that characteristically form on PFCs due to plasma-material interactions. The agreement between HYPERION and THEODOR is excellent, as the percent difference between the codes is ~5% on average in the case of the DIII-D data for moderate to high heat flux. Verification tests with TACO show slightly higher average percent differences of 8% and 12%. In using HYPERION to study filaments in heat flux, the initial results indicate that small ELMs filaments significantly broaden the divertor heat flux, and decrease divertor peak flux. Compared to the inter-ELM, the small ELM filaments decrease the divertor peak surface temperature. With intermittent divertor filaments, the divertor heat flux width is comparable with that found in L-mode.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Constrained sheath optics for high thrust density, low specific impulse ion thrusters
The results of an experimental study showing that a contoured, fine wire mesh attached to the screen grid can be used to control the divergence characteristics of ion beamlets produced at low net-to-total accelerating voltage ratios are presented. The influence of free and constrained-sheath optics systems on beamlet divergence characteristics are found to be similar in the operating regime investigated, but it was found that constrained-sheath optics systems can be operated at higher perveance levels than free-sheath ones. The concept of a fine wire interference probe that can be used to study ion beamlet focusing behavior is introduced. This probe is used to demonstrate beamlet focusing to a diameter about one hundreth of the screen grid extraction aperture diameter. Additional testing is suggested to define an optimally contoured mesh that could yield well focused beamlets at net-to-total accelerating voltage ratios below about 0.1.
Wilbur, Paul J.↗