Unstructured Triangular Grids Research Articles

Numerical Simulation of Storm Surge Inundation in Estuarine Area Considering Multiple Influencing Factors

With global climate change, the risk of extreme storms and storm surges in estuarine areas is increasing; thus, storm surge inundation research and prediction have become important issues to ensure sustainable development in estuarine areas. The Jitimen estuary in Guangdong Province, China, was chosen as our study area. In this study, a numerical model for simulating storm surge inundation in small regions based on unstructured triangular grids was established, and the model accuracy was validated. The typhoon characteristics in the study area were statistically analyzed based on historical data. Three experimental schemes, involving factors influencing storm surge inundation, such as typhoon landfall location, intensity, and direction, were used to evaluate the differences in the numerical results. The results showed that when the typhoon landfall direction remained unchanged and the highest tide levels at the Sanzao tide gauge station were similar, the differences between the numerical results for the typhoon landfall location and typhoon intensity schemes were less than 5%, and the inundation characteristics were similar. However, when the typhoon location and intensity were unchanged and the highest tide levels at the Sanzao tide gauge station were similar, the numerical results for the typhoon landfall direction scheme significantly differed; this result was caused by the difference in the duration of the high tide level (exceeding 3 m); these results indicated that the topographic characteristics and the typhoon landing direction had a greater impact on storm surge inundation. The results from this study can aid in the prediction of storm surge inundation information for the Jitimen estuary area when the typhoon landing direction and the maximum tide level are known.

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

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.

Modelling and inferring fracture curvature from borehole GPR data: A case study from the Bedretto Laboratory, Switzerland

AbstractFracture curvature has been observed from the millimetre to the kilometre scales. Nevertheless, characterizing curvature remains challenging due to data sparsity and geometric ambiguities. As a result, most numerical models often assume planar fractures to ease computations. To address this limitation, we present a novel approach for inferring fracture geometry from travel‐time data of electromagnetic or seismic waves. Our model utilizes co‐kriging interpolation of control points in a three‐dimensional surface mesh to simulate fracture curvature effectively, resulting in an unstructured triangular grid. We then refine the fracture surface into a structured grid with equidistant elements so that both small‐scale heterogeneities and large‐scale curvature can be modelled. To constrain the fracture geometry, we perform a deterministic travel‐time inversion to optimally place these control points. We validate our methodology with synthetic data and address its limitations. Finally, we infer the geometry of a large (more than 200 m) fracture observed in single‐hole ground‐penetrating radar field data. The fracture surface closely agrees with borehole televiewer observations and is also constrained far from the boreholes. Our modelling approach can be trivially adapted to multi‐offset ground‐penetrating radar or active seismic data.

A Circulation Model for Inlets Along the Central West Coast of Vancouver Island

ABSTRACT An ocean circulation model has been developed for the central west coast of Vancouver Island, with particular attention to the numerous inlets where salmon farms are located. The ultimate goal is to provide a tool to assist in informing decisions on the siting and management of fish farms and to further understanding of the regional coastal oceanography. The complicated coastline and bathymetry are approximated with an unstructured triangular grid in the horizontal direction and terrain-following coordinates in the vertical. The period of 1 March to 31 July 2016, is simulated using the Finite Volume Community Ocean Model and results are evaluated through comparisons with a combination of acoustic Doppler current profiler, tide gauge, and temperature and salinity observations. The model was found to be accurate in representing (i) tidal elevations and currents everywhere throughout the model domain and (ii) subtidal currents and temperature and salinity along the shelf. However, it fared poorly in inlets where (i) the tidal currents were relatively weak and not the dominant source of mixing and/or (ii) steep bathymetry necessitated smoothing. Sources of these and other inaccuracies, and the changes needed to overcome them, are discussed. Overall, this work highlights the complex and diverse dynamics at play in a glacially-carved coastal ocean, providing an extensive discussion of modelling challenges and potential solutions.

A numerical model for predicting waves run-up on coastal areas

ABSTRACT In this study, numerical investigations are performed to validate a numerical model for the prediction of waves propagation and waves run-up on coastal zones. The proposed numerical model is based on the depth-averaged two-dimensional dispersive shallow water equations with source terms due to variable bottom topography and bed friction effects. We propose to solve the resulting nonlinear system using a well-balanced positivity preserving Godunov-type finite volume method on unstructured triangular grids. We used a semi-implicit scheme for the friction terms and a well-balanced formulation for the bottom topography. Moreover, we prove that the numerical scheme exactly preserves a class of nontrivial steady-state solutions. To validate the proposed numerical model against experiments, we first demonstrate its ability to preserve nontrivial steady-state solutions over a slanted surface and then we model several laboratory experiments for the prediction of waves run-up on sloping beaches. The numerical simulations are in good agreement with laboratory experiments which confirms the robustness and accuracy of the proposed numerical model in predicting waves propagation on coastal areas.

A hybrid shallow water approach with unstructured triangular grids for urban flood modeling

Classic shallow water equations (SWEs) and their various simplified approaches provide the theoretical basis for urban flood modeling. Aiming at the limitations of the local inertial approach (LInA), this paper proposes a hybrid approach that combines the LInA and classic SWEs to eliminate the errors caused by LInA. Results show that the hybrid approach can reduce the error from 7% to 1.5%, with slightly reduced computation efficiency in the dam break case. In the urban flood case, the hybrid approach can reduce the relative error on flood depth from 50% to 20% in a few grids, while the relative error on flood velocity is improved from 60% to below 30%. The hybrid approach proposed here can provide a practical strategy to eliminate the errors caused by the inherent defects of the simplified approach and still maintain the computation efficiency.

SIMUG – finite element model of sea ice dynamics on triangular grid in local Cartesian basis

Abstract The paper presents the dynamical core of the new sea ice model SIMUG (Sea Ice Model on Unstructured Grid) on the A- and CD-types of unstructured triangular grids in the local-element basis on sphere. Three standardized box tests to reproduce the Linear Kinematic Features (LKFs), and the short-term forecast in the real Arctic Ocean geometry with the realistic atmosphere and ocean forcing demonstrate the model quality compared to other sea ice models like CICE, FESOM, MITgcm, and ICON-O. The distinctive features of the model presented are a wide choice of transport schemes, and the new numerical implementation with the serial and parallel C++ coding and INMOST, Ani2D, and Ani3D packages to deal with unstructured grids. Code profiling and scalability assessment are carried out. In general, the A-version of the ice drift model works faster, but has fewer degrees of freedom on the same grid. Due to the increase in the degrees of freedom, the model on the CD grid gives ultra-resolution of LKFs, but requires more strict conditions for stability.

Assessment of WAVEWATCH-III in Wind Wave Modeling of the Xisha Islands

The Xisha islands is a unique area where offshore structures can be utilized as exploration bases in the remote sea. Forecasting of sea state parameters is critical for the design and operation of offshore structures. The goal of this work is to establish an effective operational model to simulate wind waves in the Xisha Islands based on the third-generation wave model WAVEWATCH-III. During the process, two significant difficulties are highlighted and addressed: grid modeling optimization and physical source terms assessment. Typhoon-induced waves using different grid modeling techniques and physical parameterizations were modeled and evaluated using buoy measurements near islands and reefs. It was found that the unstructured triangular grid had a better performance than the other grid options in complex terrain environments like the Xisha Islands. The ST2 source-term package can provide efficient and accurate results in significant wave heights than the other source-term packages in the South China Sea.

Pemodelan Kekuatan Gelombang di Pesisir Barat Kecamatan Kuta, Bali


 
 
 
 The coastal area is an important area with many different functions for both human and marine organisms. Still, coastal regions are vulnerable to changes caused by various things, including waves. Waves can cause shoreline changes and erode coastal regions. Kuta District is one of the coastal areas on the island of Bali that are threatened with constant sediment erosion every year. One way to increase understanding of the wave and its effect on the coastal areas is through numerical modeling. This study aimed to determine the pattern of wave and wave strength distribution on the west coast of the Kuta district. The Finite Volume Coastal Ocean Model and SWAVE (FVCOM-SWAVE) coupling model that was used in this study utilized the Finite Volume method of computation with the unstructured triangular grid. The results showed that in West Season (December-January-February), the range of mean significant wave heights on the west coast of Kuta District is 0.05 - 0.2 m, and the wave power ranged from 1 to 30 W/m with the most considerable value of significant wave heights and wave power were encountered in January. Water areas near land have greater wave heights and wave power than areas far from land, except around Ngurah Rai International Airport. The movement of waves primarily comes from the southwest, the Bali Strait, to the east and is divided by the runway into following the northern and southern parts of the coast. Thus, the most significant wave height ??and wave power values are found in the waters near Kuta beach and Legian beach.
 
 
 

An efficient semi-implicit friction source term treatment for modeling overland flow

In this study, a new numerical treatment of the friction source term is proposed for modeling shallow water flows over complex bed topography. We design a novel semi-implicit temporal discretization technique based on Taylor series expansion of friction source terms. A well-balanced positivity-preserving finite volume scheme on unstructured triangular grids is used to solve the shallow water model. We present a series of numerical tests to demonstrate the robustness and effectiveness of the proposed numerical model where we used rapidly varying flows over complex topography as well as flows involving small values of water depth and wet/dry zones. The simulation results of the numerical model based on the proposed approach for friction source terms are compared to experimental data and to those obtained by using other existing techniques. The proposed numerical model is stable and second-order accurate and our predictions are in good agreement with experimental observations.

Adaptive central-upwind scheme on triangular grids for the Saint–Venant system

In this work, we develop a robust adaptive well-balanced and positivity-preserving central-upwind scheme on unstructured triangular grids for shallow water equations. The numerical method is an extension of the scheme from [{\sc Liu {\em et al.}},J. of Comp. Phys, 374 (2018), pp. 213 - 236]. As a part of the adaptive central-upwind algorithm, we obtain local a posteriori error estimator for the efficient mesh refinement strategy. The accuracy, high-resolution, and efficiency of the new adaptive central-upwind scheme are demonstrated on a number of challenging tests for shallow water models.

Сравнение способов аппроксимации функции множителей Лагранжа при решении контактных задач методом с независимой границей контакта

The paper considers the contact problem of the elasticity theory in a static spatial two-dimensional formulation without considering friction. For discretization of the elasticity theory equations, the finite element method was introduced using a triangular unstructured grid and linear and quadratic basis functions. To account for the contact boundary conditions, a modified method of Lagrange multipliers with independent contact boundary is proposed. This method implies the ability to construct a contact boundary with the smoothness degree required for the solution precision and to execute approximation of the Lagrange multiplier function independent of the grids inside the contacting bodies. Various types of the Lagrange multiplier function approximations were studied, including piecewise constant, continuous piecewise linear functions and piecewise linear functions with discontinuities at the difference cells boundaries. Examples of test calculations are provided both for problems with rectilinear and curvilinear contact boundaries. In both cases, the use of discontinuous approximations of the Lagrange multiplier function makes it possible to obtain a numerical solution with fewer artificial oscillations and higher rate of convergence at the grid refinement. It is shown that the numerical solution precision could be improved by more detailed discretization of the contact boundary without changing the grids inside the contacting bodies

A GPU-based 2D viscous flow model with variable density and heat exchange

Numerical simulation of unsteady viscous flow over variable topography under the influence of temperature changes is a challenge. In order to apply the model to large domains with complex topography, it becomes mandatory to reduce the model complexity from 3D to 2D by depth averaging the equations and to apply massive parallelization techniques for an efficient simulation. The depth averaged mass continuity, momentum and internal energy equations, combined with suitable friction laws, can be used for this type of flows. Variations in temperature can be accounted for from internal energy changes with density changing accordingly. The resulting system is solved using a finite volume technique on unstructured triangular grids well suited for problems over variable topography. A generic model applicable to a wide range of viscous fluids and validated with synthetic cases is presented to evaluate the performance of the numerical solution in presence of both external thermal forcing functions and discontinuous initial conditions. Finally, the model is applied to a realistic application and calibration to a particular case of lava flow taking into consideration variable density, viscosity and yield stress with temperature . A heat transfer with the air is included to consider the lava cooling. The numerical results of the lava front advance are compared to the Copernicus satellite observations at different dates. The efficiency of the GPU implementation allows to simulate a 11 day event in less than 1.7 h of simulation.

Seamless Integration of the Coastal Ocean in Global Marine Carbon Cycle Modeling

AbstractWe present the first global ocean‐biogeochemistry model that uses a telescoping high resolution for an improved representation of coastal carbon dynamics: ICON‐Coast. Based on the unstructured triangular grid topology of the model, we globally apply a grid refinement in the land‐ocean transition zone to better resolve the complex circulation of shallow shelves and marginal seas as well as ocean‐shelf exchange. Moreover, we incorporate tidal currents including bottom drag effects, and extend the parameterizations of the model's biogeochemistry component to account explicitly for key shelf‐specific carbon transformation processes. These comprise sediment resuspension, temperature‐dependent remineralization in the water column and sediment, riverine matter fluxes from land including terrestrial organic carbon, and variable sinking speed of aggregated particulate matter. The combination of regional grid refinement and enhanced process representation enables for the first time a seamless incorporation of the global coastal ocean in model‐based Earth system research. In particular, ICON‐Coast encompasses all coastal areas around the globe within a single, consistent ocean‐biogeochemistry model, thus naturally accounting for two‐way coupling of ocean‐shelf feedback mechanisms at the global scale. The high quality of the model results as well as the efficiency in computational cost and storage requirements proves this strategy a pioneering approach for global high‐resolution modeling. We conclude that ICON‐Coast represents a new tool to deepen our mechanistic understanding of the role of the land‐ocean transition zone in the global carbon cycle, and to narrow related uncertainties in global future projections.

Accurate Time-Domain Modeling of Arbitrarily Shaped Graphene Layers Utilizing Unstructured Triangular Grids

The accurate modeling of curved graphene layers for time-domain electromagnetic simulations is discussed in the present work. Initially, the advanced properties of graphene are presented, focusing on the propagation of strongly confined surface plasmon polariton waves at the far-infrared regime. Then, the implementation of an unstructured triangular grid was examined, based on the Delaunay triangulation method. The electric-field components were placed at the edges of the triangles, while two different techniques were proposed for the sampling of the magnetic ones. Specifically, the first one suggests that the magnetic component is placed at the triangle’s circumcenter providing more accurate results, although instability may occur for nonacute triangles. On the other hand, the magnetic field was sampled at the triangle’s centroid, considering the second technique, ensuring the algorithm’s stability, but further approximations were required, leading to a slight accuracy reduction. Moreover, the updating equations in the time-domain were extracted via an appropriate approximation of Maxwell equations in their integral form. Finally, graphene was introduced in the computational domain as an equivalent surface current density, whose location matches the corresponding electric components. The validity of our methodology was successfully performed via the comparison of graphene surface wave propagation properties to their theoretical values, whereas the global error determination indicates the minimal triangle dimensions. Additionally, an instructive setup comprising a circular graphene scatterer was analyzed thoroughly, to reveal our technique’s advantages compared to the conventional staircase discretization.

Solving two-dimensional problems of gas dynamics using an implicit scheme for the discontinuous Galerkin method on unstructured triangular grids

Solving two-dimensional problems of gas dynamics using an implicit scheme for the discontinuous Galerkin method on unstructured triangular grids

Solving Two-Dimensional Problems of Gas Dynamics Using an Implicit Scheme for the Discontinuous Galerkin Method on Unstructured Triangular Grids

Solving Two-Dimensional Problems of Gas Dynamics Using an Implicit Scheme for the Discontinuous Galerkin Method on Unstructured Triangular Grids

Модель термомиграции жидкого включения в монокристалле галитов в однородном поле градиента температуры

The paper focuses on an evolution model developed for a liquid inclusion in halites under a temperature gradient field, taking into account surface phenomena. To demonstrate the safety of heat-generating radioactive waste disposal in salt rocks (halites), thermally induced migration of liquid inclusions should be studied. Based on the study, a software package was developed providing numerical implementation of this model. The diffusion equation with initial and boundary conditions was approximated via the finite element method on triangular unstructured mobile grids. In case of weak formulation, the equations were discretized and solved in the FEniCS software. The study showed good agreement between the calculations and the experimental data.

Efficient implementation of characteristic-based schemes on unstructured triangular grids

Using characteristics to treat advection terms in time-dependent PDEs leads to a class of schemes, e.g., semi-Lagrangian and Lagrange–Galerkin schemes, which preserve stability under large Courant numbers, and may therefore be appealing in many practical situations. Unfortunately, the need of locating the feet of characteristics may cause a serious drop of efficiency in the case of unstructured space grids, and thus prevent the use of large time-step schemes on complex geometries. In this paper, we perform an in-depth analysis of the main recipes available for characteristic location, and propose a technique to improve the efficiency of this phase, using additional information related to the advecting vector field. This results in a clear improvement of execution times in the unstructured case, thus extending the range of applicability of large time-step schemes.

Optimization of Influencing Factors in Tidal Current Data Assimilation Modeling in Macro Tidal Estuary, Gyeonggi Bay, South Korea

Gu, B.-H.; Woo, S.-B., and Kim, S., 2021. Optimization of influencing factors in tidal current data assimilation modeling in macro tidal estuary, Gyeonggi Bay, South Korea. In: Lee, J.L.; Suh, K.-S.; Lee, B.; Shin, S., and Lee, J. (eds.), Crisis and Integrated Management for Coastal and Marine Safety. Journal of Coastal Research, Special Issue No. 114, pp. 66–70. Coconut Creek (Florida), ISSN 0749-0208. The study investigates the effect of the model prediction accuracy improvement using data assimilation technique in macro-tidal estuary, such as the Gyeonggi Bay (GGB), South Korea. The observation data used in this study is a tidal current measurement from Acoustic Doppler Current Profiler (ADCP) mooring device. GGB is located at the middle west coast of South Korea, and it is semi-closed estuary that has a tidal range over 6.8 m. To take the irregularity of coastline into account, this study utilized the Finite Volume Coastal Ocean Model (FVCOM), which has the flexible advantage of grid resolution by using unstructured triangular grid system. When applying data assimilation into the coastal model, various parameters, such as scaling factors and correlation lengths are needed to be adjusted to find out the best performance. Total 25 cases used in Taylor diagram showed that different influencing factors are required to be optimized at each observation location. It means that parameters in data assimilation depend on the physical dynamic system via complicated geometry. The optimized parameters not only increase by the tidal range but also it is offset by the effect of river discharge. The horizontal influence range of data assimilation with all observed locations becomes even less than the result applying only one location. It is estimated that the phenomena occurred due to strong tidal currents and interference between the range of influence. The sensitivity of data assimilation parameters in tidally dominated coastal area indicates that a systematic way of choosing the most optimized site-specific parameters are required in macro tidal area.