On Schwarz-type Smoothers for Saddle Point Problems

In this paper, the nonlinear inexact Uzawa (NIU) methods for saddle point problems are studied. A further improved convergence result of the NIU algorithm for stabilized saddle point problems is presented, which results in much smaller convergence factor. This result can also be viewed as a generalization of some previous work for classical saddle point problems. Based on this result, we generalize some adaptive versions of the NIU algorithm with variable iteration parameters for classical saddle point problems to solve stabilized saddle point problems. Convergence analyses of these algorithms are presented. It shows that they converge under similar conditions as those in classical cases, which are more practical and without estimates on the extreme eigenvalues of the involved preconditioned systems. Numerical experiments are given to demonstrate the effectiveness of these algorithms over some original NIU algorithms.

Recently, by combining the preconditioned accelerated Hermitian and skew-Hermitian splitting (PAHSS) and the parameterized Uzawa (PU) methods, Zheng and Ma (Appl Math Comput 273, 217–225, 2016b) presented the PAHSS–PU method for saddle point problems. By adding a block lower triangular matrix to the coefficient matrix on two sides of the first equation of the PAHSS–PU iterative scheme, the modified PAHSS–PU (MPAHSS–PU) iteration method is proposed in this paper, which has a faster convergence rate than the PAHSS–PU one. Furthermore, changing the position of the parameters in the MPAHSS–PU method, we develop another new method referred to as the modified PPHSS-SOR (MPPHSS-SOR) iteration method for solving saddle point problems. We provide the convergence properties of the MPAHSS–PU and the MPPHSS-SOR iteration methods, which show that the new methods are convergent if the related parameters satisfy suitable conditions. Meanwhile, practical ways to choose iteration parameters for the proposed methods are developed. Finally, numerical experiments demonstrate that the MPAHSS–PU and the MPPHSS-SOR methods outperform some existing ones both on the number of iterations and the computational times.

Saddle point problems appear in many scientific and engineering applications. Hence, it is important to solve them fast with high accuracy. We have proposed the method for saddle point problems using block structure in order to solve them fast. In our proposed method, first, a linear system with multiple right-hand sides is solved instead of solving the saddle point problems directly. After that, a small linear system with a dense matrix is solved. In our previous work, it has been observed that our method is faster than the conventional approach, but the accuracy of the obtained approximate solutions is worse than the conventional one. In this paper, we propose to improve the accuracy of the approximate solutions of the saddle point problems by improving the accuracy of the solution of the small linear system using the mixed precision iterative refinement technique. Numerical experiments illustrate that the proposed approach improves the accuracy of the approximate solutions to the same extent as the conventional approach.

As Computational Fluid Dynamics (CFD) methods evolve and mature, more engineering problems are being solved through computer simulation to reduce reliance on the costly and time-consuming experimental methods. This trend is also occurring in the gear manufacturing industry, where an increasing number of quality issues related to the oil quenching process are being investigated by CFD methods to find solutions. However, while the CFD theory and numerical methods have made significant advancements, gaps still exist between the academic research and industrial applications. In the case of the oil quenching processes, the prospect of using CFD methods to visualize and study the oil flow pattern in the gear quenching tank is promising yet challenging. The obstacle to simulating the oil quenching process using CFD methods lies not in the numerical method itself for solving the Navier-Stokes equation, but in building a computer simulation model that encompasses all the geometrical details of the quenching tank, fixtures, centrifugal pumps, and gears, including all the gear teeth. This task is particularly challenging for Finite Volume Method (FVM) CFD solvers, as the computation mesh could take days or weeks to build. In this research, a new solution method based on Smoothed Particle Hydrodynamics (SPH) is introduced to simulate the oil flow in the gear quenching tank. Since SPH is a mesh-free Lagrangian method, it not only greatly simplifies the mesh generation task for building the computational models but also handles the complex physics of the free surface flow and fluid-structure interaction with great ease. In addition, the oil flow in the gear quenching tank usually is driven by centrifugal pumps whose dynamics can be simulated directly in SPH methods, as opposed to FVM methods which require complicated moving mesh computation.

Optimal Pressure in Bypass Graft to Prevent Failure Bypass Graft in Carotid Artery to Middle Cerebral Artery Bypass using Computational Fluid Dynamic Method

Aerodynamic characteristics of a guided rocket projectile are numerically simulated. Simulations are performed in a range of flight conditions using a commercial CFD software FLUENT, and variations of lift coefficients and drag coefficients with Mach numbers and angles of attack were demonstrated. The numerical results also indicate that the angle of canard deflection has significant influence on the flow field near tailfins.

Emergency condition should be evaluated during the siting of Nuclear Power Plants (NPP). One of the criteria is the capability of emergency evacuation for the purpose of protecting the NPP staff and public. Exposure dose received by evacuees is a key factor to evaluate the effectiveness of emergency evacuation, which can be characterized by the atmospheric dispersion factors over the evacuation paths. Gaussian plume model is usually applied in the atmospheric dispersion factor calculation for NPPs. However, for some NPP sites with complex terrain like mountain and lake which has significant influence on the local flow field and the nuclides transportation, the calculations based on Gaussian model will not be accurate enough for the evaluation of the evacuation capability. In such cases, Computational Fluid Dynamics (CFD) method with fine calculation grids and rich physical models can be used in the atmospheric dispersion modeling of small-scale region, to get much more accurate results. This paper is devoted to the research on the impact of these complex terrain on atmospheric dispersion with CFD method. The local atmospheric dispersion around a NPP site located on an island is modeled, where there is a mountain on the way of evacuation. For the limitation of the geographic barrier, two evacuation paths, which are located closely with small difference in direction, are planned along different sides of the mountain. Utilizing STAR-CCM+ CFD software, local atmospheric dispersion factors are fine simulated under six worse wind directions. Based on the simulation results, the impact of the mountain on the flow field and of the radiological plume on the evacuation paths is analyzed. Results show that due to the blocking effect of the mountain, those two evacuation paths have little probability to be simultaneously covered by the radiological plume. By the choosing of suitable routes during the evacuation, the radiological risk of public is acceptable and emergency evacuation can be carried out effectively. These results also demonstrate that CFD modeling method is effective in the evaluation of local atmospheric dispersion over complex terrain, which can be applied in the analysis of emergency evacuation of NPP sites with complex terrain.

Computational modelling and experimental validation of drug entrainment in a dry powder inhaler

This paper implements the parameter identification of ship roll motion based on vibration tests and the computational fluid dynamics (CFD) method. By applying sinusoidal moment excitations from a shaker, we successfully simulate the quasi-roll motion behavior of the ship model in the air. We conduct two vibration tests, including a constant-amplitude angular displacement test and a constant-amplitude angular velocity test, to identify the restoring moment and the damping moment coefficients of the quasi-roll motion. In addition, we perform the approximate equivalence of the fluid around the ship through the CFD method and the fluid-solid coupling technique. Thus, we obtain the hydrodynamic coefficients, such as the added mass moment of inertia and the equivalent damping, to accomplish the parameter identification of the ship’s real roll motion. Finally, the accuracy of the identified parameters is verified by means of numerical simulations based on the Runge–Kutta method.

The demand for high-efficiency air vehicles and the development of distributed electric propulsion systems for aircraft are exposing the need for accurate aerodynamic prediction of multiple integrated propulsion systems. Conventional high-fidelity computational methods are too expensive, and low-cost low-fidelity methods make too many aerodynamic assumptions to be applied to these analyses. Dual-solver hybrid computational fluid dynamics (CFD) methods bridge the gap between these two categories of solvers, but many lack capabilities that are needed for complex vehicles. Recent improvements to the hybrid solver OVERFLOW-CHARM provide efficient and accurate analysis of integrated propulsion systems with hybrid CFD methods, as demonstrated on the wing–propeller system of the AIAA Workshop for Integrated Propeller Prediction. Predictions of propeller thrust are within 1% of conventional CFD data, and wing pressure coefficient distributions agree well with both experimental data and conventional CFD methods. The dual-solver results were obtained at half the computational cost of the full CFD simulation.

Modified Uzawa methods for saddle point problems

On unsymmetric block overrelaxation-type methods for saddle point problems

Fires in underground metal mines pose significant risks to worker safety and operational continuity. This study analyses the performance of the ventilation system after a fire in an underground metal mine using the Computa-tional Fluid Dynamics (CFD) method. Three different fire scenarios were modelled, examining temperature distri-bution, toxic gas dispersion, and airflow dynamics during the fire. Simulation results reveal how the fire spreads in other areas and assess the efficiency of the existing ventilation system. Findings indicate that the ventilation system is insufficient in certain areas for smoke extraction, and the post-fire gas clearance process varies across different locations. In particular, the positioning of auxiliary fans and the airflow direction are key factors in determining the spread of smoke after a fire. Based on these analyses, optimising post-fire ventilation strategies and enhancing emergency action plans are recommended. This study highlights the critical role of CFD analyses in the mining in-dustry in improving safety and efficiency and contributes to developing safer underground mine ventilation sys-tems. Furthermore, this study stands to make a substantial impact on the practical implementation of the "ventila-tion on demand" concept, advancing our understanding and application of this critical approach. On the other hand, the most important result of this study is that an underground mine with a very large volume is subject to cdf analysis as a whole. Because it is the first study to reveal that the direction of air flow changes as a fire in any part of the mine changes the thermodynamic conditions of the entire mine.

This study designed a vertical take-off and landing tailsitter unmanned aerial vehicle (UAV) with a long endurance time. Nine parameters of the tailsitter UAV were investigated. Using a 2k full factorial test, 512 experiments on the nine parameters were conducted at their maximum and minimum values. The time coefficient and air resistance were calculated using the computational fluid dynamics (CFD) method under different parameter combinations. The analysis of variance determined that the specific factors influencing the time coefficient and air resistance were the root chord, wingtip chord, wingspan, and sweep angle. By carrying out a central composite design (CCD) test, 25 sample points of the four particular factors were constructed. The time coefficient and air resistance were simulated under different structural parameter combinations using the CFD method. CFD simulation was verified by carrying out a wind tunnel test, and the results revealed that the aerodynamic coefficient error was less than 5%, while the air resistance error was less than 6%. The response surface methodology (RSM) for the time coefficient and air resistance was established using a genetic aggregation method. A multi-objective genetic algorithm (MOGA) was used to optimize the parameters with regard to the maximum time coefficient and minimum air resistance. The optimal structural parameters were wing root chord length at 315 mm, wingtip chord length at 182 mm, wingspan length at 1198 mm, and sweep angle at 16°. Compared with the original layout and size, the time coefficient of the new design of the tailsitter UAV improved by 19.5%, while the air resistance reduced by 34.78%. The results obtained by this study are significant for the design of tailsitter UAVs.

The heat dissipation of electronic elements in a mini-space is investigated by using Computational Fluid Dynamics (CFD) methods in this paper. The velocity and temperature fields of mini-space are simulated on the condition of several schemes with air as fluid. The synergetic effects of temperature and velocity field for mini-space have been analyzed by field coordination principle. Then a cooling effect number has been put forward to evaluate the cooling effects of electronic elements. The optimized scheme of mini-space has been obtained by comparing the cooling effect number of different schemes, which has established a solid foundation for discussing the cooling techniques of micro-electronic elements further.