Special adaptive grids and Runge - Richardson correction in problems with layers

При решении задач с пограничными и внутренними слоями на адаптивных сетках весьма желательно пользоваться разностными схемами, которые имеют достаточно хорошую точность и сходятся равномерно по малому параметру при стремлении шагов сетки к нулю. Однако эти требования оказываются противоречивыми: схемы высокой точности не сходятся равномерно, а равномерно сходящиеся схемы имеют обычно лишь первый порядок точности. Тем не менее существует уникальная возможность разрешить это противоречие, повышая порядок точности путем применения экстраполяционных поправок Рунге-Ричардсона, представляющих собой линейные комбинации разностных решений на вложенных сетках. В данной работе на примере нескольких употребительных разностных схем изучается эффективность такого подхода к расчетам, полученным на адаптивных сетках, явно задаваемых специальными координатными преобразованиями. Исследуются две схемы противопотокового типа с диагональным преобладанием, равномерно сходящиеся, в сравнении с аналогом схемы с центральной разностью, не имеющей диагонального преобладания и не сходящейся равномерно. Кроме простых поправок применяются также двукратные поправки, еще более повышающие порядок точности результирующих решений It is highly desirable using difference schemes with high accuracy and uniform convergence in a small parameter as the grid steps tend to zero for solving the problems with both boundary and interior layers. However, these requirements turn out to be contradictory: highly-accurate schemes may not converge uniformly, and uniformly converging schemes usually have only the first order of accuracy. Nevertheless, there is a unique opportunity to resolve this contradiction by increasing the order of accuracy by applying the Richardson-Runge extrapolation corrections, which are linear combinations of difference solutions on nested grids. In this paper, using the example of several common difference schemes, we study the efficiency of such approach for calculations obtained on adaptive grids that are explicitly specified by special coordinate transformations. Two diagonal-dominated upstream-type uniformly converging schemes are investigated. They are compared with an analogue of the scheme with central difference that does not have a diagonal dominance and does not converge uniformly. In addition to simple corrections, double corrections are also used, which further increase the order of accuracy of the resulting solutions

The interaction between a low-level jet and the boundary layer in complex topography

<p>A study investigating the effect of a low-level jet (LLJ) event on the boundary-layer (BL) turbulent structure is presented.  During a radiosounding campaign aimed at investigating the atmospheric circulation in the area of Mount Carmel and Haifa Bay in Israel (35E - 33N), characterized by a complex terrain and a winding and jagged coastline, a couple of consecutive profiles showed a significant LLJ in the morning of January 7, 2010. Since there are no previous measurements or information about frequency or characteristics of the LLJ in this region, the scarcity of observed data does not allow addressing the nature and features of the LLJ. Therefore, its characteristics and development, and also its impact on tracer dispersion, have been explored through model simulations, using RAMS atmospheric model. RAMS was configured with four nested grids with resolution from 32 km to 500 m. A high vertical resolution in the inner grid was achieved with 15 levels below 400 m, using a vertical nesting with a rather novel approach not frequently adopted. RAMS simulated variables were verified against the available observations, providing a reliable reproduction of the LLJ pattern. An elevated inversion characterized the temperature profiles and the LLJ was located at the bottom of such inversion. An analysis of the turbulence kinetic energy (TKE) versus a jet-Richardson number showed that a strongly turbulent weakly-Stable-BL was characterizing the LLJ episode. At the hours of the peak of the LLJ event, 0700 and 0800 UTC (0900 and 1000 LT), two separate maxima, generated below and above the layer affected by the LLJ, appeared in the TKE vertical profiles due to the strong wind shear. Being a morning LLJ, when buoyancy-driven vertical motions started to develop they acted sustaining the turbulence below the LLJ, then decaying at higher elevation opposed also by the strong wind speed at the LLJ level. These and other results are presented and discussed, as a contribution to the understanding of LLJ dynamics and its impact on the boundary layer in complex topography.</p>

A Wavelet-Free Approach for Multiresolution-Based Grid Adaptation for Conservation Laws

In recent years the concept of multiresolution-based adaptive discontinuous Galerkin (DG) schemes for hyperbolic conservation laws has been developed. The key idea is to perform a multiresolution analysis of the DG solution using multiwavelets defined on a hierarchy of nested grids. Typically this concept is applied to dyadic grid hierarchies where the explicit construction of the multiwavelets has to be performed only for one reference element. For non-uniform grid hierarchies multiwavelets have to be constructed for each element and, thus, becomes extremely expensive. To overcome this problem a multiresolution analysis is developed that avoids the explicit construction of multiwavelets.

Tsunami Coastal Hazard Along the Us East Coast From Coseismic Sources in the açores Convergence Zone and the Caribbean Arc Areas

We model the coastal hazard caused by tsunamis along the US East Coast (USEC) for far-field coseismic sources originated in the A\c{c}ores Convergence Zone (ACZ), and the Puerto Rico Trench (PRT)/Caribbean Arc area. In earlier work, similar modeling was performed for probable maximum tsunamis (PMTs) resulting from coseismic, submarine mass failure and volcanic collapse sources in the Atlantic Ocean basin, based on which tsunami inundation maps were developed in high hazard areas of the USEC. Here, in preparation for a future Probabilistic Tsunami Hazard Analysis (PTHA), we model a collection of 18 coseismic sources with magnitude ranging from M8 to M9 and return periods estimated in the 100-2,000 year range. Most sources are hypothetical, based on the seismo-tectonic data known for the considered areas. However, the largest sources from the ACZ, which includes the region of the Madeira Tore Rise, are parameterized as repeats of the 1755 M8.6-9 (Lisbon) earthquake and tsunami using information from many studies published on this event, which is believed to have occurred east of the MTR. Many other large events have been documented to have occurred in this area in the past 2,000 years. There have also been many large historical coseismic tsunamis in and near the Puerto Rico Trench (PRT) area, triggered by earthquakes with the largest in the past 225 years having an estimated M8.1 magnitude. In this area, coseismic sources are parameterized based on information from a 2019 USGS Powell Center expert, attended by the first author, and a collection of SIFT subfaults for the area (Gica et al., 2008). For each source, regional tsunami hazard assessment is performed along the USEC at a coarse 450 m resolution by simulating tsunami propagation to the USEC with FUNWAVE-TVD (a nonlinear and dispersive (2D) Boussinesq model), in nested grids. Tsunami coastal hazard is represented by four metrics, computed along the 5 m isobath, which quantify inundation, navigation, structural, and evacuation hazards: (1) maximum surface elevation; (2) maximum current velocity; (3) maximum momentum force; and (4) tsunami arrival time. Overall, the first three factors are larger, the larger the source magnitude, and their alongshore variation shows similar patterns of higher and lower values, due to bathymetric control from the wide USEC shelf, causing similar wave refraction patterns of focusing/defocusing for each tsunami. The fourth factor differs mostly between sources from each area (ACZ and PRT), but less so among sources from the same area; its inverse is used as a measure of increased hazard associated with short warning/evacuation times. Finally, a new tsunami intensity index (TII) is computed, that attaches a score to each metric within 5 hazard intensity classes selected for each factor, reflecting low, medium low, medium, high and highest hazard, and is computed as a weighted average of these scores (weights can be selected to reinforce the effect of certain metrics). For each source, the TII provides an overall tsunami hazard intensity along the USEC coast that allows both a comparison among sources and a quantification of tsunami hazard as a function of the source return period. At the most impacted areas of the USEC (0.1 percentile), we find that tsunami hazard in the 100-500 year return period range is commensurate with that posed by category 3-5 tropical cyclones, taking into account the larger current velocities and forces caused by tsunami waves. Based on results of this work, high-resolution inundation PTHA maps will be developed in the future, similar to the PMT maps, in areas identified to have higher tsunami hazard, using more levels of nested grids, to achieve a 10-30 m resolution along the coast.

Wind Waves in the Balaklava Bay under Extreme Wind Conditions

Wind waves in bays and harbors have a significant impact on the safety of navigation and operation of the coastal infrastructure. The purpose of this work is to study the characteristics of wind waves in the Balaklava Bay (Crimean Peninsula) under different wind conditions. The study was carried out on the basis of a numerical spectral SWAN wave model using a sequence of nested grids. Specific calculations of waves in the Balaklava Bay are carried out for constant winds of different directions and for an extreme storm emerged in the Black Sea in November 2007. It was found that in the southern part of the bay the most intense waves are formed with southerly winds. At the bay entrance, at wind speeds, which can occur once a year and once every 25 years, the maximum values of the significant wave height hs amount to 3 and 5.4 m, respectively. In the northern part of the bay, the maximum values hs with winds, which can occur once a year and once every 25 years, respectively, are equal to 0.25 and 0.46 m. It was defined that the storm waves penetrating into the southern part of the bay quickly attenuate as they spread through the narrowness to the northern part of the bay. Thus, the local wind field is the determining factor affecting the intensity of waves in the northern part of the Balaklava Bay.

Systematic comparison of different numerical approaches for tsunami simulations at the Chilean coast as part of the RIESGOS project

<p>There is a growing number of numerical models for tsunami propagation and inundation available, based on different spatial discretizations and numerical approaches. Since simulations carried out with such models are used to generate warning products in an early warning context, it is crucial to investigate differences emerging from the chosen algorithms for simulation and warning product determination. Uncertainties regarding the source determination within the first minutes after a tsunami generation might be of major concern for an appropriate warning at the coast, still, the sensitivity of warning products with respect to pre-computed simulation database contents or on-the-fly calculations are of crucial importance as well.</p><p>In this study, we investigate the performance of three models (TsunAWI, HySEA, COMCOT) in the oceanic region offshore central and northern Chile with inundation studies in Valparaíso and Viña del Mar. The investigation forms part of the tsunami component in the RIESGOS project dealing more general with multi hazard assessments in the Andes region. The numerical implementation of the models include both a finite element approach with triangular meshes of variable resolution as well as finite difference implementations with nested grids for the coastal area. The tsunami sources are identical in all models and chosen from an ensemble of events used in an earlier probabilistic study of the region. Additionally, two historic events are considered as well to validate the models against the corresponding measurements.</p><p>We compare results in virtual gauges as well as actual tide gauge locations at the Chilean coast. Inundation areas are determined with high resolution and employing the model specific wetting and drying implementations. We compare the model results and sensitivities with respect to spatial resolution and parameters like bottom friction and bathymetry  representation in the varying mesh geometries.</p>

Transformasi Gelombang Swell dan Gelombang Angin di Perairan Selatan Bali (Hal. 28-39)

ABSTRAKGelombang swell dengan energi yang besar dan dapat menjalar hingga ratusan kilometer dari daerah pembangkitannya diketahui berpotensi merusak struktur pantai dan juga dapat mengganggu segala aktivitas yang dilakukan di pantai. Gelombang swell juga dinyatakan memberikan pengaruh yang besar pada inundasi yang terjadi di sepanjang pantai selatan Jawa dan Bali pada tanggal 4-9 Juni 2006 (Nugraheni, dkk., 2017). Studi transformasi gelombang swell dan gelombang angin di perairan selatan Bali dilakukan dengan pemodelan numerik gelombang menggunakan model gelombang generasi ketiga SWAN model. Simulasi dilakukan dengan tiga nested grid dengan resolusi grid #1, #2 dan #3; masing-masing sebesar 0.05o, 0.005o, dan 0.001o. Simulasi dilakukan untuk dua buah skema pemodelan, yaitu model gelombang swell dan model gelombang angin. Hasil model menunjukan kesesuaian dengan data pengamatan. Hasil simulasi memperlihatkan gelombang swell yang berasal dari Samudera Hindia mendominasi kondisi gelombang di perairan selatan Bali selama periode simulasi (18 Desember 2011-6 Februari 2012). Dibandingkan dengan gelombang angin, gelombang swell menghasilkan tinggi gelombang yang lebih besar baik di lepas pantai maupun di area dekat pantai. Gelombang swell mengalami refraksi yang kuat di sekitar Bukit Peninsula.Kata kunci: gelombang Swell, gelombang angin, pemodelan transformasi gelombang. ABSTRACTSwells with its large energy can propagate up to hundreds of kilometers from the generation location. Therefore, swells have the potential to damage the structure of the coast and also can disrupt all activities carried out on the coast. Swells were also stated to have a major influence on the inundation that occurred along the southern coast of Java and Bali on June 4 to 9, 2006 (Nugraheni, et al., 2017). The study of swells and wind waves transformations in the waters of southern Bali is carried out by numerical wave modeling using a third generationwave model SWAN model. Nested grids are used with spatial resolution of grid #1, #2 and #3; is 0.05o, 0.005o, and 0.001o, respectively. Simulations are carried out for two modeling schemes that areswell models and wind wave models. The simulation shows compliance with observation data. The result shows swells originating from the Indian Ocean mostly dominated wave conditions in the waters of southern Bali during simulation period (18 Desember 2011-6 Februari 2012). Compared to wind waves, swells produce higher wave both in offshore and coastal area. Swells experienced a strong refraction around the Bukit Peninsula.Keywords: swell, wind wave, wave transformation model.