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Improved ALE mesh velocities for complex flows

A key choice in the development of arbitrary Lagrangian-Eulerian solution algorithms is how to move the computational mesh. The most common approaches are smoothing and relaxation techniques, or to compute a mesh velocity field that produces smooth mesh displacements. We present a method in which the mesh velocity is specified by the irrotational component of the fluid velocity as computed from a Helmholtz decomposition, and excess compression of mesh cells is treated through a noniterative, local spring-force model. This approach allows distinct and separate control over rotational and translational modes. In conclusion, the utility of the new mesh motion algorithm is demonstrated on a number of 3D test problems, including problems that involve both shocks and significant amounts of vorticity.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Potential alteration of fjordal circulation due to a large floating structure—Numerical investigation with application to Hood Canal basin in Puget Sound

Circulation in typical fjords is characterized by a shallow brackish layer at the surface over a deep long and narrow saltwater column. This surface layer is responsible for the outflow of water from the fjord, is easily disrupted by external forces, such as wind, and is influenced by freshwater inflow. In this paper, we postulate that the stability of fjordal circulation may also be vulnerable to impacts from anthropogenic alterations, such as floating structures, that could constrict the mixing and transport in the upper layers of the water column. The potential for alteration of circulation in Hood Canal, a silled-fjord located inside Puget Sound, Washington, has been examined. Using classical analytical treatments along the lines formulated by Hansen and Rattray [1965], Rattray [1967], Dyer [1973] and more recently, MacCready [2004], we develop a solution applicable to a range of estuary classifications varying from a partially mixed estuary regime to classical fjord conditions. Both estuary types exist in the Puget Sound system, and we compare our analytical solution with observed data. The analysis is based on an exponential variation of eddy viscosity with depth, and it has been extended further with modifications of the free surface boundary conditions to develop a solution representing the presence of a floating bridge at the estuary/fjord entrance. The model results show that tidally averaged mean circulation under the influence of such a constraint could reduce by as much as 30 to 50 percent. The overall water quality of fjords and narrow estuaries is dependent on net circulation and flushing. A potential decrease in residual flow or a corresponding increase in residence time of this magnitude merits further study.

3D hydrodynamic model, Unstructured grid, FVCOM, F↗

TokaMaker: An open-source time-dependent Grad-Shafranov tool for the design and modeling of axisymmetric fusion devices

Here, in this paper, we present a new static and time-dependent MagnetoHydroDynamic (MHD) equilibrium code, TokaMaker, for axisymmetric configurations of magnetized plasmas, based on the well-known Grad-Shafranov equation. This code utilizes finite element methods on an unstructured triangular grid to enable capturing accurate machine geometry and simple mesh generation from engineering-like descriptions of present and future devices. The new code is designed for ease of use without sacrificing capability and speed through a combination of Python, Fortran, and C/C++ components. A detailed description of the numerical methods of the code, including a novel formulation of the boundary conditions for free-boundary equilibria, and validation of the implementation of those methods using both analytic test cases and cross-code validation is shown. Results show expected convergence across tested polynomial degree for analytic and cross-code test cases.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

ThinCurr: An open-source 3D thin-wall eddy current modeling code for the analysis of large-scale systems of conducting structures

In this paper we present a new thin-wall eddy current modeling code, ThinCurr, for studying inductively-coupled currents in 3D conducting structures -- with primary application focused on the interaction between currents flowing in coils, plasma, and conducting structures of magnetically-confined plasma devices. The code utilizes a boundary finite element method on an unstructured, triangular grid to accurately capture device structures. The new code, part of the broader Open FUSION Toolkit, is open-source and designed for ease of use without sacrificing capability and speed through a combination of Python, Fortran, and C/C++ components. Scalability to large models is enabled through use of hierarchical off-diagonal low-rank compression of the inductance matrix, which is otherwise dense. Ease of handling large models of complicated geometry is further supported by automatic determination of supplemental elements through a greedy homology approach. Here, a detailed description of the numerical methods of the code and verification of the implementation of those methods using cross-code comparisons against the VALEN code and Ansys commercial analysis software is shown.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Wave climate and energy resources in the Mariana Islands from a 42-year high-resolution hindcast

We report a high-resolution wave hindcast from 1979 to 2020 was developed for Guam and the Commonwealth of the Northern Mariana Islands, which are influenced by mesoscale and synoptic weather systems from the western Pacific Rim to the Central Pacific. The spectral wave modeling utilized structured global and unstructured regional grids with improved resolution in nearshore waters, where wave resources development is most feasible. The hindcast demonstrates its capability in capturing multi-modal seas through reproduction of bulk and partitioned wave parameters derived from altimetry and buoy measurements. The local wave climate is influenced by the year-round trade winds and tropical cyclones as well as seasonal monsoons, frontal systems, and mid-latitude high- and low-pressure systems. The strong intra-annual variation of the significant wave height and power flux reflects transitions between local and distant weather systems, which account for the diverse wave conditions comprised of short-period wind waves, intermediate-period seas, and long-period swells around the islands. Among the Pacific island regions, spectral partitioning is particularly important for describing the dominant wave components by period and direction with pertinent information conducive to energy resources characterization and coastal zone management in the Mariana Islands.

16 TIDAL AND WAVE POWER↗

Salish Sea Response to Global Climate Change, Sea Level Rise, and Future Nutrient Loads

Given annual occurrences of hypoxia, harmful algal blooms, and evidence of coastal acidification, the potential impacts of climate change on water quality are of increasing concern in the U.S. Pacific Northwest estuaries such as the Salish Sea. While large-scale global climate projections are well documented, our understanding of the nearshore estuarine-scale response is not as well developed. In this study, the future response within the Salish Sea fjord-like environment was examined using the Salish Sea Model driven by downscaled outputs from the NCAR climate model CESM. We simulated a single projection of 95-year change under the RCP 8.5 greenhouse gas emissions scenario. Results indicate that higher temperatures, lower pH, and decreased dissolved oxygen levels in the upwelled shelf waters in the future would propagate into the Salish Sea. Results point to potential changes in average Salish Sea temperature (≈+1.51°C), dissolved oxygen (≈-0.77 mg/L), and pH (acidification -0.18 units) in the Y2095 relative to historical Y2000. The algal biomass in the Salish Sea could increase by ≈23% with a potential species shift from diatoms towards dinoflagellates. The region of annually recurring hypoxia could increase from <1% today to ≈16% in the future. Finally, the results suggest that the future response in the Salish Sea is less severe relative to the change predicted near the continental shelf boundary. This resilience of the Salish Sea may be attributed to the existence of strong vertical circulation cells that provide mitigation and serve as a physical buffer, thus keeping waters cooler, more oxygenated, and less acidic.

54 ENVIRONMENTAL SCIENCES↗

A simple dynamic subgrid-scale model for LES of particle-laden turbulence

In this study, a dynamic model for large-eddy simulations is proposed in order to describe the motion of small inertial particles in turbulent flows. The model is simple, involves no significant computational overhead, contains no adjustable parameters, and is flexible enough to be deployed in any type of flow solvers and grids, including unstructured setups. The approach is based on the use of elliptic differential filters to model the subgrid-scale velocity. The only model parameter, which is related to the nominal filter width, is determined dynamically by imposing consistency constraints on the estimated subgrid energetics. The performance of the model is tested in large-eddy simulations of homogeneous-isotropic turbulence laden with particles, where improved agreement with direct numerical simulation results is observed in the dispersed-phase statistics, including particle acceleration, local carrier-phase velocity, and preferential-concentration metrics.

42 ENGINEERING↗

Nonconforming Mesh Refinement for High-Order Finite Elements

In this study, we propose a general algorithm for nonconforming adaptive mesh refinement (AMR) of unstructured meshes in high-order finite element codes. Our focus is on $h$-refinement with a fixed polynomial order. The algorithm handles triangular, quadrilateral, hexahedral, and prismatic meshes of arbitrarily high-order curvature, for any order finite element space in the de Rham sequence. We present a flexible data structure for meshes with hanging nodes and a general procedure to construct the conforming interpolation operator, both in serial and in parallel. The algorithm and data structure allow anisotropic refinement of tensor product elements in two and three dimensions and support unlimited refinement ratios of adjacent elements. We report numerical experiments verifying the correctness of the algorithms and perform a parallel scaling study to show that we can adapt meshes containing billions of elements and run efficiently on 393,000 parallel tasks. Finally, we illustrate the integration of dynamic AMR into a high-order Lagrangian hydrodynamics solver.

97 MATHEMATICS AND COMPUTING↗

Sandia Unstructured Triangle Tabular Interpolation Package v 0.1 beta

The software interpolates tabular data, such as for equations of state, provided on an unstructured triangular grid. In particular, interpolation occurs in a two dimensional space by looking up the triangle in which the desired evaluation point resides and then performing a linear interpolation over the n-tuples associated with the nodes of the chosen triangle. The interface to the interpolation routines allows for automated conversion of units from those tabulated to the desired output units. when multiple tables are included in a data file, new tables may be generated by on-the-fly mixing of the provided tables

Carpenter, JohnH.↗

Sandia Unstructured Triangle Table Generator

The software generates data tables for thermodynamic and transport properties of materials as described by a set of input models. For each input model parameterization, an associated table is created on an unstructured triangular grid. These grids all conform to the same topology. A statistical accuracy guarantee is provided for the tabular representation of the model. Details of the model and table specification are given in a XML input deck.

Carpenter, JohnH.↗

High-Resolution Regional Atmosphere–Ocean–Wave Coupled Simulations of Hurricane Henri (2021)

To explore the integrated effects of ocean and ocean surface wave related physical processes on TC simulations, a set of three model simulations is performed. * In experiment 'A', the event is modeled using the Weather Research Forecasting (WRF) model alone with prescribed Sea Surface Temperature (SST) at 6-hour intervals. * In experiment ‘AO,’ WRF is coupled with the Finite Volume Community Ocean Model (FVCOM), enabling variable exchange between atmosphere and ocean, but without considering ocean surface wave-related physical processes. * In experiment ‘AOW’, WRF, FVCOM, and Simulating WAves Nearshore (SWAN) exchange variables with each other every hour through the OASIS3-MCT Coupler to allow direct and indirect atmosphere-ocean-wave interactions. * Observational data are also included in this dataset (Dropsonde, HRD-Radar, NDBC_wave). All simulations are initialized at 18:00 UTC on August 19, 2021, within a domain encompassing the western North Atlantic Ocean. The atmospheric domain features a horizontal resolution of 3 km. The ocean domain, which covers a substantial portion of the WRF ocean domain, employs an unstructured triangular grid with resolutions ranging from 3 km near the coast to 9 km in the open ocean, effectively resolving the complex coastline of the U.S. Northeast Coast. Initial and boundary conditions for the atmosphere model are obtained from the 6-hourly 0.25° NCEP (National Centers for Environmental Prediction) Global Forecast System (GFS; NCEP, 2015) data.

17 WIND ENERGY↗

High-Resolution Regional Atmosphere–Ocean–Wave Coupled Simulations of Hurricane Henri (2021)

To explore the integrated effects of ocean and ocean surface wave related physical processes on TC simulations, a set of three model simulations is performed. * In experiment 'A', the event is modeled using the Weather Research Forecasting (WRF) model alone with prescribed Sea Surface Temperature (SST) at 6-hour intervals. * In experiment ‘AO,’ WRF is coupled with the Finite Volume Community Ocean Model (FVCOM), enabling variable exchange between atmosphere and ocean, but without considering ocean surface wave-related physical processes. * In experiment ‘AOW’, WRF, FVCOM, and Simulating WAves Nearshore (SWAN) exchange variables with each other every hour through the OASIS3-MCT Coupler to allow direct and indirect atmosphere-ocean-wave interactions. * Observational data are also included in this dataset (Dropsonde, HRD-Radar, NDBC_wave). All simulations are initialized at 18:00 UTC on August 19, 2021, within a domain encompassing the western North Atlantic Ocean. The atmospheric domain features a horizontal resolution of 3 km. The ocean domain, which covers a substantial portion of the WRF ocean domain, employs an unstructured triangular grid with resolutions ranging from 3 km near the coast to 9 km in the open ocean, effectively resolving the complex coastline of the U.S. Northeast Coast. Initial and boundary conditions for the atmosphere model are obtained from the 6-hourly 0.25° NCEP (National Centers for Environmental Prediction) Global Forecast System (GFS; NCEP, 2015) data.

17 WIND ENERGY↗

High-Resolution Regional Atmosphere–Ocean–Wave Coupled Simulations of Hurricane Henri (2021)

To explore the integrated effects of ocean and ocean surface wave related physical processes on tropical cyclone simulations, a set of three model simulations is performed. * In experiment 'A', the event is modeled using the Weather Research Forecasting (WRF) model alone with prescribed Sea Surface Temperature (SST) at 6-hour intervals. * In experiment ‘AO,’ WRF is coupled with the Finite Volume Community Ocean Model (FVCOM), enabling variable exchange between atmosphere and ocean, but without considering ocean surface wave-related physical processes. * In experiment ‘AOW’, WRF, FVCOM, and Simulating WAves Nearshore (SWAN) exchange variables with each other every hour through the OASIS3-MCT Coupler to allow direct and indirect atmosphere-ocean-wave interactions. * Observational data are also included in this dataset (Dropsonde, HRD-Radar, NDBC_wave). All simulations are initialized at 18:00 UTC on August 19, 2021, within a domain encompassing the western North Atlantic Ocean. The atmospheric domain features a horizontal resolution of 3 km. The ocean domain, which covers a substantial portion of the WRF ocean domain, employs an unstructured triangular grid with resolutions ranging from 3 km near the coast to 9 km in the open ocean, effectively resolving the complex coastline of the U.S. Northeast Coast. Initial and boundary conditions for the atmosphere model are obtained from the 6-hourly 0.25° NCEP (National Centers for Environmental Prediction) Global Forecast System (GFS; NCEP, 2015) data. These CSV files are derived from the NetCDF files in the c0 dataset. Unlike the original format, where geographic coordinates were stored in a separate file, each CSV now embeds the corresponding latitude and longitude values alongside the measured or simulated variables.

17 WIND ENERGY↗

High-resolution Hindcasts for U.S. Wave Energy Resource Characterization

The marine and hydrokinetic (MHK) industry is at an early stage of development and has the potential to play a significant role in diversifying the U.S. energy portfolio and reducing the U.S. carbon footprint. Wave energy is the largest among all the U.S. MHK energy resources, which include wave energy, ocean current, tidal-instream, ocean thermal energy conversion, and river-instream. Wave resource characterization is an essential step for regional wave energy assessments, Wave Energy Converter (WEC) project development, site selection and WEC design. The present paper provides an overview of a joint modelling effort by the Pacific Northwest National Laboratory and Sandia National Laboratories on high-resolution wave hindcasts to support the U.S. Department of Energy’s Water Power Technologies Office’s program of wave resource characterization, assessment and classifications in all US coastal regions. Topics covered include the modelling approach, model input requirements, model validation strategies, high performance computing resource requirements, model outputs and data management strategies. Examples of model setup and validation for different regions are provided along with application to development of classification systems, and analysis of regional wave climates. Lessons learned and technical challenges of the long-term, high-resolution regional wave hindcast are discussed.

Yang, Zhaoqing↗

Finite difference operators on unstructured triangular meshes

A new form of the Laplace operator is derived which is shown to be second-order accurate when calculated at mesh triangle nodes if the cells corresponding to the nodes have a high degree of symmetry. It is demonstrated that the Laplace operator directly derived from Stokes' integral theorem is only zeroth-order accurate on these same cells. The construction of gradient and Laplace operators on unstructured triangular grids are discussed from the variational point of view. Two discrete representations of the Laplacian are compared to each other, and conclusions are drawn regarding their accuracy on a pointwise basis. Finally, geometric relations valid on arbitrary polygons are given for completeness in an appendix.

Erlebacher, G.↗

An adaptive finite element method for high speed flows

The solution of the equations of compressible high speed flow, on unstructured triangular grids in 2D and tetrahedral grids in 3D, is considered. Solution methods based upon both Taylor-Galerkin and Runge-Kutta time-stepping techniques are presented and the incorporation of the ideas of flux corrected transport (FCT) is discussed. These methods are combined with an adaptive mesh regeneration procedure and are employed in the solution of several examples, consisting of Euler flows in both 2D and 3D and Navier-Stokes flows in 2D.

Peraire, J.↗

Calculations of rotational flows using stream function

The stream function equation is solved for steady two-dimensional (and axisymmetric) rotational flows. Both finite differences and finite volumes discretization techniques are studied, using generalized body fitted coordinates and unstructured staggered grids, respectively. For inviscid transonic flows, a new artificial viscosity scheme which does not produce any artificial vorticity is introduced, for the stability of the mixed flow calculations and for capturing shocks. The solution of Euler equations, in primitive variables, are also considered. The effects of the artificial viscosity and numerical boundary conditions on the total enthalpy and the vorticity distributions are demonstrated.

Hafez, M.↗