Conservative and bounded volume-of-fluid advection on unstructured grids
Not Available
Ivey, Christopher B. (ORCID:0000000300087532)↗
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Results for “Unstructured Grids”
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A multiscale restriction-smoothed basis method for high contrast porous media represented on unstructured grids
A wide variety of multiscale methods have been proposed in the literature to reduce runtime and provide better scaling for the solution of Poisson-type equations modeling flow in porous media. We present a new multiscale restricted-smoothed basis (MsRSB) method that is designed to be applicable to both rectilinear grids and unstructured grids. Like many other multiscale methods, MsRSB relies on a coarse partition of the underlying fine grid and a set of local prolongation operators (multiscale basis functions) that map unknowns associated with the fine grid cells to unknowns associated with blocks in the coarse partition. These mappings are constructed by restricted smoothing: Starting from a constant, a localized iterative scheme is applied directly to the fine-scale discretization to compute prolongation operators that are consistent with the local properties of the differential operators. The resulting method has three main advantages: First of all, both the coarse and the fine grid can have general polyhedral geometry and unstructured topology. This means that partitions and good prolongation operators can easily be constructed for complex models involving high media contrasts and unstructured cell connections introduced by faults, pinch-outs, erosion, local grid refinement, etc. In particular, the coarse partition can be adapted to geological or flow-field properties represented on cells or faces to improve accuracy. Secondly, the method is accurate and robust when compared to existing multiscale methods and does not need expensive recomputation of local basis functions to account for transient behavior: Dynamic mobility changes are incorporated by continuing to iterate a few extra steps on existing basis functions. This way, the cost of updating the prolongation operators becomes proportional to the amount of change in fluid mobility and one reduces the need for expensive, tolerance-based updates. Finally, since the MsRSB method is formulated on top of a cell-centered, conservative, finite-volume method, it is applicable to any flow model in which one can isolate a pressure equation. Herein, we only discuss single and two-phase incompressible models. Compressible flow, e.g., as modeled by the black-oil equations, is discussed in a separate paper.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Model Test Bed for Evaluating Unstructured-Grid Wave Models for Resource Assessment and Characterization
Recent development of unstructured-grid wave models demonstrates the advantage of using an unstructured-grid modeling framework in wave modeling, especially in coastal areas that have complex coastlines, islands, shallow-water bays, and estuaries. This study evaluated the performance of unstructured-grid models in comparison to structured-grid models for predicting the IEC wave energy resource parameters at a common test bed site. Model skill was assessed using a set of model performace error statistics. Sensitivity of open boundary conditions and ]wind forcing on model results, computational efficiency, and the advantage and limitation of the unstructured-grid model are summarized in the report.
16 TIDAL AND WAVE POWER↗
Wave Resource Characterization Using an Unstructured Grid Modeling Approach
This paper presents a modeling study conducted on the central Oregon coast for wave resource characterization using the unstructured-grid SWAN model coupled with a nested-grid WWIII model. The flexibility of models of various spatial resolutions and the effects of open- boundary conditions simulated by a nested-grid WWIII model with different physics packages were evaluated. The model results demonstrate the advantage of the unstructured-grid modeling approach for flexible model resolution and good model skills in simulating the six wave resource parameters recommended by the International Electrotechnical Commission in comparison to the observed data in Year 2009 at National Data Buoy Center Buoy 46050. Notably, spectral analysis indicates that the ST4 physics package improves upon the model skill of the ST2 physics package for predicting wave power density for large waves, which is important for wave resource assessment, device load calculation, and risk management. In addition, bivariate distributions show the simulated sea state of maximum occurrence with the ST4 physics package matched the observed data better than that with the ST2 physics package. This study demonstrated that the unstructured-grid wave modeling approach, driven by the nested-grid regional WWIII outputs with the ST4 physics package, can efficiently provide accurate wave hindcasts to support wave resource characterization. Our study also suggests that wind effects need to be considered if the dimension of the model domain is greater than approximately 100 km, or O (10^2 km).
Wu, Wei-Cheng↗
A Numerical Study of Hypoxia in Chesapeake Bay Using an Unstructured Grid Model: Validation and Sensitivity to Bathymetry Representation
A three-dimensional unstructured-grid hydrodynamic and water quality model (Semi-implicit Cross-scale Hydroscience Intergrated System Model-Integrated Compartment Model) is applied successfully for Chesapeake Bay. The model is validated with observations of salinity, chlorophyll-a, dissolved oxygen, nutrients, and phytoplankton productions from the year 1991 to 1995 for the mainstem and some major tributaries, based on multiple model skill scores. Model experiments are conducted to test the importance of having (1) an accurate representation of bathymetry to correctly predict hypoxia and other processes and (2) a high-resolution model grid for tributaries to correctly simulate water quality variables. Further, comparison with the model experiment results with bathymetry smoothing indicates that bathymetry smoothing, as commonly used for many systems, changes the stratification and lateral circulation pattern, resulting in more salt intrusion into shallow water regions, and an increase in the freshwater age. Consequently, a model with bathymetry smoothing can lead to an unrealistic prediction of the distribution of hypoxia and phytoplankton production. Local grid refinement shows significant improvement of model simulations on local stratification and water quality variables. Overall, the use of high-resolution unstructured grid model leads to a faithful representation of the complex geometry, and thus a seamless cross-scale capability for simulating water quality processes in the Bay including tributaries and tidal creeks.
54 ENVIRONMENTAL SCIENCES↗
Global seamless tidal simulation using a 3D unstructured-grid model (SCHISM v5.10.0)
We present a new 3D unstructured-grid global ocean model to study both tidal and nontidal processes, with a focus on the total water elevation. Unlike existing global ocean models, the new model resolves estuaries and rivers down to ~8 m without the need for grid nesting. The model is validated with both satellite and in situ observations for elevation, temperature, and salinity. Tidal elevation solutions have a mean complex root-mean-square error (RMSE) of 4.2 cm for M2 and 5.4 cm for all five major constituents in the deep ocean. The RMSEs for the other four constituents, S2, N2, K1, and O1, are, respectively, 2.05, 0.93, 2.08, and 1.34 cm). The nontidal residual assessed by a tide gauge dataset (GESLA) has a mean RMSE of 7 cm. For the first time ever, we demonstrate the potential for seamless simulation on a single mesh from the global ocean into several estuaries along the US West Coast. The model is able to accurately capture the total elevation, even at some upstream stations. The model can therefore potentially serve as the backbone of a global tide surge and compound flooding forecasting framework.
54 ENVIRONMENTAL SCIENCES↗
An improved multislope MUSCL scheme for solving shallow water equations on unstructured grids
In this paper we describe an improved vector manipulation multislope monotone upstream-centred scheme for conservation laws (MUSCL) reconstruction for solving the shallow water equations on unstructured grids. This improved MUSCL reconstruction method includes a bigger stencil for the interpolation and saves time for determining the geometric relations compared to the original vector manipulation method, so it is computationally more efficient and straightforward to implement. Four examples involving an analytical solution, laboratory experiments and field-scale measurements are used to test the performance of the proposed scheme. It has been proven that the proposed scheme can provide comparable accuracy and higher efficiency compared to the original vector manipulation method. With the increasing of the number of cells, the advantage of the proposed scheme becomes more apparent.
42 ENGINEERING↗
Improved multislope MUSCL reconstruction on unstructured grids for shallow water equations
In shallow water flow and transport modeling, the monotonic upstream-centered scheme for conservation laws (MUSCL) is widely used to extend the original Godunov scheme to second-order accuracy. The most important step in MUSCL-type schemes is MUSCL reconstruction, which calculate-extrapolates the values of independent variables from the cell center to the edge. The monotonicity of the scheme is preserved with the help of slope limiters that prevent the occurrence of new extrema during reconstruction. On structured grids, the calculation of the slope is straightforward and usually based on a 2-point stencil that uses the cell centers of the neighbor cell and the so-called far-neighbor cell of the edge under consideration. On unstructured grids, the correct choice for the upwind slope becomes nontrivial. 2 novel total variation diminishing schemes are developed based on different techniques for calculating the upwind slope and the downwind slope. An additional treatment that stabilizes the scheme is discussed. The proposed techniques are compared to 2 existing MUSCL reconstruction techniques, and a detailed discussion of the results is given. Finally, it is shown that the proposed MUSCL reconstruction schemes obtain more accurate results with less numerical diffusion and higher efficiency.
54 ENVIRONMENTAL SCIENCES↗
Tracer transport within an unstructured grid ocean model using characteristic discontinuous Galerkin advection
Not Available
97 MATHEMATICS AND COMPUTING↗
Asynchronous Navier-Stokes Solver on 3D Unstructured Grids for the Exascale Era
This project has developed multiple fluid dynamics solvers for complex 3D flows using fully asynchronous distributed-memory task-parallel algorithms on top of the Charm++ runtime system. The algorithms solve the Euler or Navier-Stokes equations of compressible flows using unstructured tetrahedron meshes with optional solution-adaptive mesh-, and polynomial-order refinement. We have demonstrated excellent strong scaling up 50K compute cores and the benefits of Charm++’s automatic load balancing.
97 MATHEMATICS AND COMPUTING↗
A new high-order spectral difference method for simulating viscous flows on unstructured grids with mixed-element meshes
In the present study, a spectral difference (SD) method is developed for viscous flows on meshes with a mixture of triangular and quadrilateral elements. The standard SD method for triangular elements, which employs Lagrangian interpolating functions for fluxes, is not stable when the designed accuracy of spatial discretization is third order or higher. Unlike the standard SD method, the method examined here uses vector interpolating functions in the Raviart-Thomas (RT) spaces to construct continuous flux functions on reference elements. The spectral-difference Raviart-Thomas (SDRT) method was originally proposed by Balan et al. and implemented on triangular-element meshes for invisid flow only. Our present results demonstrated that the SDRT method is stable and high-order accurate in two dimensions (2D) for a number of test problems by using triangular-, quadrilateral-, and mixed-element meshes for both inviscid and viscous flows. A stability analysis is also performed for mixed elements. Furthermore, we found our current SDRT scheme is stable for fourth-order accurate spatial discretizations. However, a stable fifth-order SDRT scheme remains to be identified.
97 MATHEMATICS AND COMPUTING↗
A hybrid reconstructed discontinuous Galerkin and continuous Galerkin finite element method for incompressible flows on unstructured grids
Not Available
Pandare, Aditya K. (ORCID:0000000301637321)↗
Benchmarking an unstructured grid sediment model in an energetic estuary
Not Available
54 ENVIRONMENTAL SCIENCES↗
First benchmark of the Unstructured Grid Adaptation Working Group.
Abstract not provided.
Ibanez, Daniel Alejandro↗
A Pipeline for Large Data Processing Using Regular Sampling for Unstructured Grids
Large simulation data requires a lot of time and computational resources to compute, store, analyze, visualize, and run user studies. Today, the largest cost of a supercomputer is not hardware but maintenance, in particular energy consumption. Our goal is to balance energy consumption and cognitive value of visualizations of resulting data. This requires us to go through the entire processing pipeline, from simulation to user studies. To reduce the amount of resources, data can be sampled or compressed. While this adds more computation time, the computational overhead is negligible compared to the simulation time. We built a processing pipeline at the example of regular sampling. The reasons for this choice are two-fold: using a simple example reduces unnecessary complexity as we know what to expect from the results. Furthermore, it provides a good baseline for future, more elaborate sampling methods. We measured time and energy for each test we did, and we conducted user studies in Amazon Mechanical Turk (AMT) for a range of different results we produced through sampling.
97 MATHEMATICS AND COMPUTING↗
OpenACC directive-based GPU acceleration of an implicit reconstructed discontinuous Galerkin method for compressible flows on 3D unstructured grids
In this study, we use a combination of modeling techniques to describe the relationship between fracture radius that might be accomplished in a hypothetical enhanced geothermal system (EGS) and drilling distance required to create and access those fractures. We use a combination of commonly applied analytical solutions for heat transport in parallel fractures and 3D finite-element method models of more realistic heat extraction geometries. For a conceptual model involving multiple parallel fractures developed perpendicular to an inclined or horizontal borehole, calculations demonstrate that EGS will likely require very large fractures, of greater than 300 m radius, to keep interfracture drilling distances to ~10 km or less. As drilling distances are generally inversely proportional to the square of fracture radius, drilling costs quickly escalate as the fracture radius decreases. It is important to know, however, whether fracture spacing will be dictated by thermal or mechanical considerations, as the relationship between drilling distance and number of fractures is quite different in each case. Information about the likelihood of hydraulically creating very large fractures comes primarily from petroleum recovery industry data describing hydraulic fractures in shale. Those data suggest that fractures with radii on the order of several hundred meters may, indeed, be possible. The results of this study demonstrate that relatively simple calculations can be used to estimate primary design constraints on a system, particularly regarding the relationship between generated fracture radius and the total length of drilling needed in the fracture creation zone. Comparison of the numerical simulations of more realistic geometries than addressed in the analytical solutions suggest that simple proportionalities can readily be derived to relate a particular flow field.
15 GEOTHERMAL ENERGY↗
A New High-Order Spectral Difference Method for Simulating Viscous Flows on Unstructured Grids with Mixed Elements
In the present study, a new spectral difference (SD) method is developed for viscous flows on meshes with a mixture of triangular and quadrilateral elements. The standard SD method for triangular elements, which employs Lagrangian interpolating functions for fluxes, is not stable when the designed accuracy of spatial discretization is third-order or higher. Unlike the standard SD method, the method examined here uses vector interpolating functions in the Raviart-Thomas (RT) spaces to construct continuous flux functions on reference elements. Studies have been performed for 2D wave equation and Euler equa- tions. Our present results demonstrated that the SDRT method is stable and high-order accurate for a number of test problems by using triangular-, quadrilateral-, and mixed- element meshes.
17 WIND ENERGY↗