Valid Physical Processes from Numerical Discontinuities in Computational Fluid Dynamics

Due to the limited cell resolution in the representation of flow variables, a piecewise continuous initial reconstruction with discontinuous jump at a cell interface is usually used in modern computational fluid dynamics methods. Starting from the discontinuity, a Riemann problem in the Godunov method is solved for the flux evaluation across the cell interface in a finite volume scheme. With the increasing of Mach number in the CFD simulations, the adaptation of the Riemann solver seems introduce intrinsically a mechanism to develop instabilities in strong shock regions. Theoretically, the Riemann solution of the Euler equations are based on the equilibrium assumption, which may not be valid in the non-equilibrium shock layer. In order to clarify the flow physics from a discontinuity, the unsteady flow behavior of one-dimensional contact and shock wave is studied on a time scale of (0~10000) times of the particle collision time. In the study of the non-equilibrium flow behavior from a discontinuity, the collision-less Boltzmann equation is first used for the time scale within one particle collision time, then the direct simulation Monte Carlo (DSMC) method will be adapted to get the further evolution solution. The transition from the free particle transport to the dissipative Navier-Stokes (NS) solutions are obtained as an increasing of time. The exact Riemann solution becomes a limiting solution with infinite number of particle collisions. For the high Mach number flow simulations, the points in the shock transition region, even though the region is enlarged numerically to the mesh size, should be considered as the points inside a highly non-equilibrium shock layer

An investigation on the effects of increasing maximum wind speed of tropical cyclones on the return periods of water levels in the sea area of the Yangtze River Delta

This paper investigates the impact of increasing maximum wind speed of tropical cyclones on the return periods of water levels in the sea area of the Yangtze River Delta. To conduct this study, a series of numerical experiments are performed using historical tropical cyclones that impacted the Yangtze River Delta from 1949 to 2019. The aim is to analyze the effects of global climate change on extreme water levels and the corresponding return periods. To obtain the historical water levels in the sea areas of the Yangtze River Delta, a storm surge model is driven by the selected tropical cyclones. The simulated astronomical tidal levels during the same period are also used. The extreme water levels of different return periods are then calculated. The maximum wind speeds of the selected tropical cyclones are increased by 11% according to the expected amount of increase under global climate change. The extreme water levels of different return periods under this scenario are calculated with the same procedure. The results of the study show that the impact of increasing maximum wind speed of tropical cyclones on the increases of extreme water levels and the decrease of return periods is more significant in the inner area of the estuaries than in the outer areas. Moreover, the responses of the extreme water levels and the corresponding return periods in the Yangtze River Estuary and the Hangzhou Bay show different characteristics. The results of this study provide significant reference value for the management of future coastal disaster prevention and mitigation in the Yangtze River Delta. Furthermore, the methodology used in this study can be applied in other estuaries to investigate the potential impacts of changes in climate and hydrology factors on extreme water levels and the corresponding return periods

Simulation of vapor flows in short path distillation

Based on the direct simulation Monte Carlo (DSMC) method, one- and two-dimensional models of vapor flows in the short path distillation are established. To reflect the reality, molecular rotation is included in this study and a reasonable boundary condition is introduced. The simulations are tested by comparison with the previous experiment, which shows that the distillation rate and composition are closer to the experiment compared to the previous models, and the simulated temperature field is higher than that of the previous models. The agreements between experimental and simulated results show that the models represent well the phenomena that occur in the vapor space of the short path distillatory. Based on the revised model, macroscopic variables related to a particular position in the distillation gap are analyzed in detailed. Furthermore, dependence of the evaporation efficiency on the ratio of condensing area to evaporating area and influence of inert gas on the distillation process are investigated. (C) 2012 Elsevier Ltd. All rights reserved

Real-time correction of channel-bed roughness and water level in river network hydrodynamic modeling for accurate forecasting

Abstract The accuracy and reliability of hydrodynamic models are sensitive to both hydraulic state variables and model parameters, particularly the bed roughness, while their simultaneous real-time corrections and corresponding effects still need to be well-established and understood. This paper presents a real-time data assimilation model that corrects channel-bed roughness and water level in a river network hydrodynamic model, ensuring its accuracy and reliability. Experiments and parameter analysis evaluated the effect of initial roughness and observation noise level on model performance. Correcting both roughness and water level improved filtering time and forecasting accuracy by up to 63% and 80%, respectively, compared to methods only correcting water level. The filtering time was reduced by 44–63%, and the water level forecasting RMSE decreased by up to 80%. Both models experienced increased filtering time and forecasting error as observation noise increased, but the proposed model had a lower increase. With accurate hydraulic state measurement (e.g., 0.005 m error), the model achieved negligible water level forecasting error after 7 h of data assimilation. The model's accuracy depended on the initial channel-bed roughness, and the algorithm enables real-time roughness correction, making it useful for flood forecasting

Cross-Scale Modeling of Shallow Water Flows in Coastal Areas with an Improved Local Time-Stepping Method

A shallow water equations-based model with an improved local time-stepping (LTS) scheme is developed for modeling coastal hydrodynamics across multiple scales, from large areas to detailed local regions. To enhance the stability of the shallow water model for long-duration simulations and at larger LTS gradings, a prediction-correction method using a single-layer interface that couples coarse and fine time discretizations is adopted. The proposed scheme improves computational efficiency with an acceptable additional computational burden and ensures accurate conservation of time truncation errors in a discrete sense. The model performance is verified with respect to conservation and computational efficiency through two idealized tests: the spreading of a drop of shallow water and a tidal flat/channel system. The results of both tests demonstrate that the improved LTS scheme maintains precision as the LTS grading increases, preserves conservation properties, and significantly improves computational efficiency with a speedup ratio of up to 2.615. Furthermore, we applied the LTS scheme to simulate tides at grid scales of 40,000 m to 200 m for a portion of the Northwest Pacific. The proposed model shows promise for modeling cross-scale hydrodynamics in complex coastal and ocean engineering problems

Risk Level Assessment of Typhoon Hazard Based on Loss Utility

In the context of climate change with frequent natural disasters, disaster risk assessment can provide great help for related risk decision-making. Based on the theory of loss expectation, this paper presents a quantitative method to assess typhoon disaster risk. Among them, the probability of typhoon occurrence is calculated by fitting the optimal structure function of the sample to the joint distribution of wave height, water increment and wind speed. Then, the loss expectation is expressed as the product of typhoon occurrence probability and loss utility, which is used to quantify the loss result of a typhoon disaster. Using the loss utility theory, the risk grade chart is drawn with the direct economic loss rate and the proportion of the affected population as indicators. The results show that the absolute loss value considering the loss utility is slightly higher than the loss value of the quantitative algorithm by 2% to 25%, indicating that the new model reflects the social group’s aversion to typhoon disaster risk. As can be seen from the risk level zoning map, the highest combined risk level typhoons are Prapiroon 0606 and Chanthu 1003, with a risk level of Category 5. The typhoon comprehensive risk level before 2011 was ≥3, and the typhoon comprehensive risk level from 2012 to 2015 was ≤3. The evaluation model has certain feasibility and practicability, and the results can provide a basis and reference for typhoon risk assessment and decision-making

Elevation Calculation of Bottom Deck Based on Stochastic Process and Compound Distribution

In the design of offshore platforms, the height of the bottom deck directly affects the safety and engineering cost of the entire platform. It is a very important scale parameter in platform planning. The American Petroleum Institute (API) specification shows that the key to determining the height of the bottom deck lies in the wave height and calculation of the return level of the water increase. Based on the perspective of stochastic processes, this paper constructs a new distribution function model for joint parameter estimation of the marine environment. The new model uses a family of random variables to show the statistical characteristics of design wave height and water increase in both time and space, with extreme value expanded EED-I type distribution used as marginal distribution. The new model performs statistical analysis on the measured hydrological data of the Naozhou Station during the flood period from 1990 to 2016. The Gumbel–Copula structure function is used as the connection function, and the compound distribution model of the wave height and the water increase is used to obtain the joint return level of the wave height and the water increase and through which the bottom deck height of the area is calculated. The results show that the stochastic compound distribution improves the issue of the high design value caused by simple superposition of univariate return levels. The EED-I type distribution still has good stability under the condition of less measured data. Thus, under the premise of ensuring the safety of the offshore platform, less measured data can still be used to calculate the height of the bottom deck more accurately