Local time-stepping for the shallow water equations using CFL optimized forward-backward Runge-Kutta schemes
Not Available
97 MATHEMATICS AND COMPUTING↗
Engineering topics
Engwirda, Darren
Publications and source records attributed to Engwirda, Darren.
Simulation of Compound Flooding Using River‐Ocean Two‐Way Coupled E3SM Ensemble on Variable‐Resolution Meshes
Abstract Coastal zone compound flooding (CF) can be caused by the interactive fluvial and oceanic processes, particularly when coastal backwater propagates upstream and interacts with high river discharge. The modeling of CF is limited in existing Earth System Models (ESMs) due to coarse mesh resolutions and one‐way coupled river‐ocean components. In this study, we present a novel multi‐scale coupling framework within the Energy Exascale Earth System Model (E3SM), integrating global atmosphere and land with interactively coupled river and ocean models using different meshes with refined resolutions near the coastline. To evaluate this framework, we conducted ensemble simulations of a CF event (Hurricane Irene in 2011) in a Mid‐Atlantic estuary. The results demonstrate that the novel E3SM configuration can reasonably reproduce river discharge and sea surface height variations. The two‐way river‐ocean coupling improves the representation of coastal backwater effects at the terrestrial‐aquatic interface that are caused by the combined actions of tide and storm surge during the CF event, thus providing a valuable modeling tool for better understanding the river‐estuary‐ocean dynamics in extreme events under climate change. Notably, our results show that the most significant CF impacts occur when the highest storm surge generated by a tropical cyclone meets with a moderate river discharge. This study highlights the state‐of‐the‐art advancements developed within E3SM for simulating multi‐scale coastal processes.
54 ENVIRONMENTAL SCIENCES↗
MPAS - Ocean Simulation Quality for Variable-Resolution North American Coastal Meshes
Climate model components utilizing unstructured meshes enable variableresolution, regionally enhanced simulations within global domains. Here we investigate the relationship between mesh quality and simulation statistics using the JIGSAW unstructured meshing library and the Model for Prediction Across ScalesOcean (MPASOcean) with a focus on Gulf Stream dynamics. In the base configuration, the refined region employs 8 km cells that extend 400 km from the coast of North America. This coastal refined region is embedded within a lowresolution global domain, with cell size varying latitudinally between 30 and 60 km. The resolution transition region between the refined region and background mesh is 600 km wide. Three sensitivity tests are conducted: 1) the quality of meshes is intentionally degraded so that horizontal cells are progressively more distorted; 2) the transition region from high to low resolution is steepened; and 3) resolution of the coastal refinement region is varied from 30 km to 8 km. Overall, the ocean simulations are shown to be robust to mesh resolution and quality alterations. Meshes that are substantially degraded still produce realistic currents, with Southern Ocean transports within 0.4% and Gulf Stream transports within 12% of highquality mesh results. The narrowest transition case of 100 km did not produce any spurious effects. Refined regions with high resolution produce eddy kinetic energy and sea surface height variability that are similar to the highresolution reference simulation. These results provide heuristics for the design criteria of variableresolution climate model domains.
Hoch, Kristin E.↗
Using Power Diagrams to Build Optimal Unstructured Meshes for C-Grid Models
The Model for Prediction Across Scales (MPAS) for Ocean (-O), Sea-Ice (-SI) and Land-Ice (-LI), in addition to the Coastal Ocean Marine Prediction Across Scales (COMPAS) are two novel general circulation models designed to resolve coupled ocean-ice dynamics over variable spatial scales using non-uniform unstructured grids. Both models are based on a conservative mimetic finite-difference/volume formulation (TRiSK), in which staggered momentum, vorticity and mass-based degrees- of-freedom are distributed over an orthogonal 'primal-dual' mesh.
Engwirda, Darren↗
Generalised Primal-Dual Grids for Unstructured Co-Volume Schemes
The generation of high-quality staggered unstructured grids is considered, leading to the development of a new optimisation-based strategy designed to construct weighted 'Regular-Power' tessellations appropriate for co-volume type numerical discretisation techniques. This new framework aims to extend the conventional Delaunay-Voronoi primal-dual structure; seeking to assemble generalised orthogonal tessellations with enhanced geometric quality. The construction of these grids is motivated by the desire to improve the performance and accuracy of numerical methods based on unstructured co-volume type schemes, including various staggered grid techniques for the simulation of fluid dynamics and hyperbolic transport. In this study, a new hybrid optimisation strategy is proposed; seeking to optimise the geometry, topology and weights associated with general, two-dimensional Regular-Power tessellations using a combination of gradient-ascent and energy-based techniques. The performance of this new method is tested experimentally, with a range of complex, multi-resolution primal-dual grids generated for various coastal and regional ocean modelling applications.
power diagrams↗
JIGSAW-GEO (1.0): Locally Orthogonal Staggered Unstructured Grid Generation for General Circulation Modelling on the Sphere
An algorithm for the generation of non-uniform, locally orthogonal staggered unstructured spheroidal grids is described. This technique is designed to generate very high-quality staggered VoronoiDelaunay meshes appropriate for general circulation modelling on the sphere, including applications to atmospheric simulation, ocean-modelling and numerical weather prediction. Using a recently developed Frontal-Delaunay refinement technique, a method for the construction of high-quality unstructured spheroidal Delaunay triangulations is introduced. A locally orthogonal polygonal grid, derived from the associated Voronoi diagram, is computed as the staggered dual. It is shown that use of the Frontal-Delaunay refinement technique allows for the generation of very high-quality unstructured triangulations, satisfying a priori bounds on element size and shape. Grid quality is further improved through the application of hill-climbing-type optimisation techniques. Overall, the algorithm is shown to produce grids with very high element quality and smooth grading characteristics, while imposing relatively low computational expense. A selection of uniform and non-uniform spheroidal grids appropriate for high-resolution, multi-scale general circulation modelling are presented. These grids are shown to satisfy the geometric constraints associated with contemporary unstructured C-grid-type finite-volume models, including the Model for Prediction Across Scales (MPAS-O). The use of user-defined mesh-spacing functions to generate smoothly graded, non-uniform grids for multi-resolution-type studies is discussed in detail.
geophysical fluid dynamics↗
Multi-Resolution Unstructured Grid-Generation for Geophysical Applications on the Sphere
An algorithm for the generation of non-uniform unstructured grids on ellipsoidal geometries is described. This technique is designed to generate high quality triangular and polygonal meshes appropriate for general circulation modelling on the sphere, including applications to atmospheric and ocean simulation, and numerical weather predication. Using a recently developed Frontal-Delaunay-refinement technique, a method for the construction of high-quality unstructured ellipsoidal Delaunay triangulations is introduced. A dual polygonal grid, derived from the associated Voronoi diagram, is also optionally generated as a by-product. Compared to existing techniques, it is shown that the Frontal-Delaunay approach typically produces grids with near-optimal element quality and smooth grading characteristics, while imposing relatively low computational expense. Initial results are presented for a selection of uniform and non-uniform ellipsoidal grids appropriate for large-scale geophysical applications. The use of user-defined mesh-sizing functions to generate smoothly graded, non-uniform grids is discussed.
Weather↗
Voronoi-Based Point-Placement for Three-Dimensional Delaunay-Refinement
An extension of the restricted Delaunay-refinement algorithm for three-dimensional tetrahedral mesh generation is described, in which an off-centre type point-placement scheme is utilised. It is shown that the use of generalised Steiner points, positioned along edges in the associated Voronoi complex, typically leads to improvements in the overall size, quality and grading of the resulting tetrahedral meshes. The new algorithm can be viewed as a Frontal-Delaunay approach - a hybridisation of conventional Delaunay-refinement and advancing-front techniques, in which new vertices are positioned to satisfy both element size- and shapeconstraints. The new method is shown to inherit many of the best features of classical Delaunay-refinement and advancing-front type algorithms, combining good practical performance with theoretical robustness. Experimental comparisons show that
algorithms↗