TWO-GRID WEAK GALERKIN METHOD FOR SEMILINEAR ELLIPTIC DIFFERENTIAL EQUATIONS

In this paper, we investigate a two-grid weak Galerkin method for semilinear elliptic differential equations. The method mainly contains two steps. First, we solve the semi-linear elliptic equation on the coarse mesh with mesh size H, then, we use the coarse mesh solution as a initial guess to linearize the semilinear equation on the fine mesh, i.e., on the fine mesh (with mesh size $h$), we only need to solve a linearized system. Theoretical analysis shows that when the exact solution u has sufficient regularity and $h=H^2$, the two-grid weak Galerkin method achieves the same convergence accuracy as weak Galerkin method. Several examples are given to verify the theoretical results.

On locally embedded two-scale solution for wall-bounded turbulent flows

Recent findings on wall-bounded turbulence have prompted a new impetus for modelling development to capture and resolve the Reynolds-number-dependent influence of outer flow on near-wall turbulence in terms of the ‘foot-printing’ of the large-scale coherent structures and the scale-interaction associated ‘modulation’. We develop a two-scale method to couple a locally embedded near-wall fine-mesh direct numerical simulation (DNS) block with a global coarser mesh domain. The influence of the large-scale structures on the local fine-mesh block is captured by a scale-dependent coarse–fine domain interface treatment. The coarse-mesh resolved disturbances are directly exchanged across the interface, while only the fine-mesh resolved fluctuations around the coarse-mesh resolved variables are subject to periodic conditions in the streamwise and spanwise directions. The global near-wall coarse-mesh region outside the local fine-mesh block is governed by the augmented flow governing equations with forcing source terms generated by upscaling the space–time-averaged fine-mesh solution. The validity and effectiveness of the method are examined for canonical incompressible channel flows at several Reynolds numbers. The mean statistics and energy spectra are in good agreement with the corresponding full DNS data. The results clearly illustrate the ‘foot-printing’ and ‘modulation’ in the local fine-mesh block. Noteworthy also is that neither spectral-gap nor scale-separation is assumed, and a smooth overlap between the global-domain and the local-domain energy spectra is observed. It is shown that the mesh-count scaling with Reynolds number is potentially reduced from $O(R{e^2})$ for the conventional fully wall-resolved large-eddy simulation (LES) to $O(Re)$ for the present locally embedded two-scale LES.

Evaluation of Mei-yu heavy-rainfall quantitative precipitation forecasts in Taiwan by a cloud-resolving model for three seasons of 2012–2014

In this study, the performance of quantitative precipitation forecasts (QPFs) by the Cloud-Resolving Storm Simulator (CReSS) in Taiwan, at a horizontal grid spacing of 2.5 km and a domain size of 1500×1200 km2, in the range of 1–3 d during three Mei-yu seasons (May–June) of 2012–2014 is evaluated using categorical statistics, with an emphasis on heavy-rainfall events (≥100 mm per 24 h). The categorical statistics are chosen because the main hazards are landslides and floods in Taiwan, so predicting heavy rainfall at the correct location is important. The overall threat scores (TSs) of QPFs for all events on day 1 (0–24 h) are 0.18, 0.15, and 0.09 at thresholds of 100, 250, and 500 mm, respectively, and indicate considerable improvements at increased resolution compared to past results and 5 km models (TS < 0.1 at 100 mm and TS ≤ 0.02 at 250 mm). Moreover, the TSs are shown to be higher and the model more skillful in predicting larger events, in agreement with earlier findings for typhoons. After classification based on observed rainfall, the TSs of day − 1 QPFs for the largest 4 % of events by CReSS at 100, 250, and 500 mm (per 24 h) are 0.34, 0.24, and 0.16, respectively, and can reach 0.15 at 250 mm on day 2 (24–48 h) and 130 mm on day 3 (48–72 h). The larger events also exhibit higher probability of detection and lower false alarm ratio than smaller ones almost without exception across all thresholds. With the convection and terrain better resolved, the strength of the model is found to lie mainly in the topographic rainfall in Taiwan rather than migratory events that are more difficult to predict. Our results highlight the crucial importance of cloud-resolving capability and the size of fine mesh for heavy-rainfall QPFs in Taiwan.

Design and Operation of “Siklob”, a Mechanised Falling Gear Operated in Northern Iloilo, Philippines

Fisheries in the Philippines is multispecies, and this is seen with the wide variety of fishing gears used in major and minor fishing grounds in the country. These gears constantly face modification and development to improve catch quality, quantity, and overall efficiency. This study investigated the features of “siklob”, a mechanised falling gear operated along the municipal waters of Northern Iloilo, Philippines. Some coastal residents claimed that fishers use fine mesh nets for this gear, and this was because of some incidences of the capture of very small fish. Results of this study, however, indicate that the mesh size of nettings used for “siklob” is 4.35 cm, which is above the minimum set by the national law (3 cm). The gear is operated offshore, in a fishing vessel, with lights and fish-finding devices. The catch included an array of pelagic to benthic species, with Sardinella gibbosa (Bleeker, 1849) as the top species. The catch per unit effort values for two fishing operations were 17.40 kg.cast-1 and 16.5 kg.cast-1, respectively. If a management plan for the gear is to be implemented in the area, it would be necessary first to study the spawning seasons of commercially important species and impose closed fishing seasons. Before any attempt to ban or control the use of the gear, it is necessary first to understand the gear design, performance, and selectivity.

A diagnostic study of flood producing rainstorm of September 1988 over northwest India with the aid of a fine mesh numerical analysis system

A numerical analysis of the synoptic situation leading to devastating floods in Punjab and adjoining states during September 1988 has been carried out. The analysis is done by three dimensional multivariate optimum interpolation (OI) scheme cast on 1° x 1° Lat./Long. Grid. Software has been developed for computation of several derived parameters and linked with the basic flow variable analysis. A diagnostic study of day-to-day rainfall versus the objectively analysed grid point fields of integrated horizontal flux divergence of water vapour is carried out, The study brings out a close spatial correspondence between the area of net moisture flux convergence on the analysis day and the area of heavy rainfall on the following day. The study suggests that the numerical analysis products can be of a good predictive value to a synoptic forecaster In heavy rainfall predictions under difficult and uncertain synoptic situations.

Impact of parameterized convection on a numerically simulated tropical Cyclone structure

ABSTRACT. Condensational heating is a primary source of energy for disturbances like a tropical storm. The resolvable scale condensation and the parameterized convection, in many fine mesh numerical models, are evaluated at intervals greater than the time step, order of a minute, used for computing dynamical processes. The latent heating may depend on the model resolution and the interval at which the precipitation physics is evaluated. Numerical results from a series of short range forecasts are compared to study the impact of varying the horizontal resolution and the interval for evaluating condensation physics, and of excluding the parameterized convective heating. A horizontal grid spacing of 40 km (coarse mesh) or 20 km (fine mesh) in National Centers for Environmental Prediction's Quasi-Lagrangian Model (QLM), and the initial data for a tropical storm case, are utilized. Resolvable scale condensation is invoked only at supersaturated grid points, and a Kuo-type convective parameterization procedure is employed. Significant structural differences are produced when the interval for computing both parameterized convection and resolvable scale heating is changed, and these differences broaden when the horizontal resolution is increased. The central warm cote structure and storm intensity are simulated better when both condensational processes are evaluated at an interval of twelve time steps than at each time step. Vertical columns in central storm area rapidly become convectively stable, and the maximum in vertical motion and strongest horizontal winds shift in the outer storm area, when both condensational processes are invoked at each time step. The central storm area remains conditionally unstable, and strongest winds develop close to the center, when both condensational processes are evaluated at intervals of twelve time steps. The central storm area remains conditionally unstable also in the fine mesh experiment in which the parameterized convective heating is excluded and the resolvable scale heating is evaluated at each time step. Intense vertical motion and vigorous heating develop in deep vertical columns, indicating that the heating on the convective scale is simulated as the resolvable scale heating. The vertical distribution of heating and the storm structure, during the first six hours in this case, are similar to those in the fine mesh run in which both condensational processes are evaluated at intervals of twelve time steps. However, the storm intensifies more rapidly after 6 h in the former than in the later case. Numerical results from additional experiments are presented to show that predicted storm structure is modified with a change in interval for invoking either or both condensational processes, and these circulation differences are not due to the initial spin up. Transfer of moisture and heat from low levels into the higher troposphere in cumulonimbus clouds takes place in several minutes. Above cited and other predictions from the QLM suggest that storm structure. intensity and motion in a mesoscale model are likely to, be improved when parameterized convective heating is included; however, a parameterization scheme that concurrently produces alterations in the entire model cloud depth should be invoked at intervals of several minutes.

RANS-BASED CFD PREDICTION OF THE HYDRODYNAMIC COEFFICIENTS OF DARPA SUBOFF GEOMETRY IN STRAIGHT-LINE AND ROTATING ARM MANOEUVRES

Computational Fluid Dynamics (CFD) simulations using Reynolds Averaged Navier-Stokes (RANS) equations are increasingly adopted as an analysis tool to predict the hydrodynamic coefficients of underwater vehicles. These simulations have shown to offer both a high degree of accuracy comparable to experimental methods and a greatly reduced computational cost compared to Large Eddy Simulation (LES) and Direct Numerical Simulation (DNS). However, one of the major challenges faced with CFD simulations is that the results can vary greatly depending on the numerical model settings. This paper uses the DARPA SUBOFF hull form undergoing straight-line and rotating arm manoeuvres at different drift angles to analyse the hydrodynamic forces and moments on the vehicle against experimental data, showing that the selection of the boundary conditions and turbulence models, and the quality of the mesh model can have a considerable and independent effect on the computational results. Comparison between the Baseline Reynolds Stress Model (BSLRSM) and Shear Stress Transport with Curvature Correction (SSTCC) were carried out for both manoeuvres, showing that with a sufficiently fine mesh, appropriate mesh treatment, and simulation conditions matching the experiments; the BSLRSM predictions offer good agreement with experimental measurements, while the SSTCC predictions are agreeable with the longitudinal force but fall outside the experimental uncertainty for both the lateral force and yawing moment.

Study of Crater in the Gobi Desert Induced by Ground Explosion of Large Amounts of TNT Explosive up to 10 Tons

Explosion craters on the ground surface induced by contact or near-field explosions have important implications, which can be used to assess blast consequences, guide the design of the explosion, or develop a protective strategy. In this study, to understand the crater characteristics induced by the contact explosion of large weight explosives, four field contact explosion tests were conducted on the surface of the Gobi Desert with large TNT charge weights of 1 ton, 3 tons, and 10 tons (test conducted twice). Cratering on the ground surface generated by large amounts of explosives was measured and evaluated, including the shape, depth, and diameter. A fine-mesh numerical model was developed and validated on the AUTODYN software platform, and a detailed parametric study was performed on the resulting craters. The effects of sand and gravel density, initiation method, shear modulus, and failure criteria were analyzed and discussed. An energy conversion coefficient was determined, and the corresponding theoretical equations were derived to predict the dimensions of the craters resulting from the large weight contact explosion. The calculated cratering characteristics were consistent with previous data and hence can be used in future engineering applications.

Anaerobic Digestion for Biogas Production from Municipal Sewage Sludge: A Comparative Study between Fine Mesh Sieved Primary Sludge and Sedimented Primary Sludge

Two different types of primary sewage sludge have been used as feedstock for production of biogas through anaerobic digestion (AD): the one type was sludge from a typical primary clarifier (PC), while the other type of sludge produced by a rotating belt filter, commonly called microsieve (MS). Initially the main physicochemical characteristics of the sludges, such as total solids (TS), volatile solids (VS), VS/TS, pH and carbon to nitrogen ratio (C/N) were determined, for MS: 37.86 ± 0.08%, 83.00 ± 0.41%, 0.83 ± 0.00, 6.67 ± 0.08 and 19.68 ± 0.69, respectively, and for PC: 2.61 ± 0.08%, 78.77 ± 1.91%, 0.79 ± 0.02, 6.61 ± 0.10 and 14.46 ± 1.23, respectively. Then, calculated amounts of the sludges were inserted into airtight vials and were inoculated using anaerobic sludge. The daily biogas production was measured over a period of 30 days. PC sludge maximized the daily biogas production (44.20 mlbiogas/gvsd) 11 days after inoculation, while the MS sludge reach a peak (37.74 mlbiogas/gvsd) 14 days after inoculation. The cumulative biogas production over the 30 days of AD was in the same laver (442.29 mlbiogas/gvs for PC versus 434.73 mlbiogas/gvs for MS). However, PC sludge indicated higher daily biogas production, compared to MS sludge, while the opposite was observed for the period following the peak point. The Volatile Solids Reduction for PC and MS sludges was recorded as 46.06% and 32.39%, respectively.

No Difference in Instream Decomposition Among Upland Agricultural and Forested Streams in Kenya

Expansion of agriculture is particularly worrying in tropical regions of the world, where native forests have been replaced by croplands and grasslands, with severe consequences for biodiversity conservation and ecosystem functioning. However, limited data exist on the effects of agriculture on the functioning of tropical streams. We conducted a leaf litter decomposition experiment in coarse- and fine-mesh litterbags using the three species of leaves (Eucalyptus globulus [non-native], Vernonia myriantha, and Syzygium cordatum [indigenous]) in three forested and agricultural streams to determine the effect of agriculture on instream leaf litter decomposition in headwater stream sites. We also examined the functional composition of macroinvertebrates in the streams through the contents of benthic kick samples. Agricultural streams had a less dense riparian canopy and smaller abundance of coarse organic particulate matter, and higher electric conductivity and suspended solids than forested streams. In terms of the effects of litter quality on decomposition rates, Vernonia had the fastest decomposition rates while Eucalyptus had the slowest in both forested and agricultural sites. Shredder invertebrates were less abundant in agricultural streams, and in both stream types, they were less diverse and abundant than other functional groups. Overall, leaf litter decomposition rates did not respond to agricultural land-use. The hypothesized negative effects of agriculture on organic matter processing were minimal and likely modulated by intact riparian zones along agricultural streams.