Reduction of Numerical Oscillations in Simulating Moving-Boundary Problems by the Local DFD Method

In this work,the hybrid solution reconstruction formulation proposed by Luo et al.[H.Luo,H.Dai,P.F.de Sousa and B.Yin,On the numerical oscillation of the direct-forcing immersed-boundary method for moving boundaries,Computers&Fluids,56(2012),pp.61–76]for the finite-difference discretization on Cartesian meshes is implemented in the finite-element framework of the local domain-free discretization(DFD)method to reduce the numerical oscillations in the simulation of movingboundary flows.The reconstruction formulation is applied at fluid nodes in the immediate vicinity of the immersed boundary,which combines weightly the local DFD solution with the specific values obtained via an approximation of quadratic polynomial in the normal direction to the wall.The quadratic approximation is associated with the no-slip boundary condition and the local simplified momentum equation.The weighted factor suitable for unstructured triangular and tetrahedral meshes is constructed,which is related to the local mesh intervals near the immersed boundary and the distances from exterior dependent nodes to the boundary.Therefore,the reconstructed solution can account for the smooth movement of the immersed boundary.Several numerical experiments have been conducted for two-and three-dimensional moving-boundary flows.It is shown that the hybrid reconstruction approach can work well in the finite-element context and effectively reduce the numerical oscillations with little additional computational cost,and the spatial accuracy of the original local DFD method can also be preserved.

Implementation of a particle-in-cell method for the energy solver in 3D spherical geodynamic modeling

The thermal evolution of the Earth’s interior and its dynamic effects are the focus of Earth sciences.However,the commonly adopted grid-based temperature solver is usually prone to numerical oscillations,especially in the presence of sharp thermal gradients,such as when modeling subducting slabs and rising plumes.This phenomenon prohibits the correct representation of thermal evolution and may cause incorrect implications of geodynamic processes.After examining several approaches for removing these numerical oscillations,we show that the Lagrangian method provides an ideal way to solve this problem.In this study,we propose a particle-in-cell method as a strategy for improving the solution to the energy equation and demonstrate its effectiveness in both one-dimensional and three-dimensional thermal problems,as well as in a global spherical simulation with data assimilation.We have implemented this method in the open-source finite-element code CitcomS,which features a spherical coordinate system,distributed memory parallel computing,and data assimilation algorithms.

Hybrid N-order Lagrangian Interpolation Eulerian-Lagrangian Method for Salinity Calculation

The Eulerian？Lagrangian method（ELM） has been used by many ocean models as the solution of the advection equation,but the numerical error caused by interpolation imposes restriction on its accuracy.In the present study,hybrid N-order Lagrangian interpolation ELM（Li ELM） is put forward in which the N-order Lagrangian interpolation is used at first,then the lower order Lagrangian interpolation is applied in the points where the interpolation results are abnormally higher or lower.The calculation results of a step-shaped salinity advection model are analyzed,which show that higher order（N=3？8） Li ELM can reduce the mean numerical error of salinity calculation,but the numerical oscillation error is still significant.Even number order Li ELM makes larger numerical oscillation error than its adjacent odd number order Li ELM.Hybrid N-order Li ELM can remove numerical oscillation,and it significantly reduces the mean numerical error when N is even and the current is in fixed direction,while it makes less effect on mean numerical error when N is odd or the current direction changes periodically.Hybrid odd number order Li ELM makes less mean numerical error than its adjacent even number order Li ELM when the current is in the fixed direction,while the mean numerical error decreases as N increases when the current direction changes periodically,so odd number of N may be better for application.Among various types of Hybrid N-order Li ELM,the scheme reducing N-order directly to 1st-order may be the optimal for synthetic selection of accuracy and computational efficiency.

Solving the Sod Shock Tube Problem Using Localized Differential Quadrature (LDQ) Method

The localized differential quadrature (LDQ) method is a numerical technique with high accuracy for solving most kinds of nonlinear problems in engineering and can overcome the difficulties of other methods (such as difference method) to numerically evaluate the derivatives of the functions.Its high efficiency and accuracy attract many engineers to apply the method to solve most of the numerical problems in engineering.However,difficulties can still be found in some particular problems.In the following study,the LDQ was applied to solve the Sod shock tube problem.This problem is a very particular kind of problem,which challenges many common numerical methods.Three different examples were given for testing the robustness and accuracy of the LDQ.In the first example,in which common initial conditions and solving methods were given,the numerical oscillations could be found dramatically;in the second example,the initial conditions were adjusted appropriately and the numerical oscillations were less dramatic than that in the first example;in the third example,the momentum equation of the Sod shock tube problem was corrected by adding artificial viscosity,causing the numerical oscillations to nearly disappear in the process of calculation.The numerical results presented demonstrate the detailed difficulties encountered in the calculations,which need to be improved in future work.However,in summary,the localized differential quadrature is shown to be a trustworthy method for solving most of the nonlinear problems in engineering.

NUMERICAL STUDY OF THE SHORT-TERM CLIMATIC OSCILLATION FORCED BY EL NINO DURING NORTHERN WINTER

Using a nine-layer global spectral model, numerical schemes with two different SST distributions in January (control case and abnormal case) have been tested to study the climatic effect, propagation charateris- tics and the maintenance mechanism of the short-term climatic oscillation caused by El Nino during northern winter. The main results are as follows: (1) During northern winter, there exist two wave trains because of the influence of El Nino. One is similar to PNA pattern, and the other is similar to EUP pattern. (2) The PNA-like wave train caused by the anomalous SST forcing in central and eastern equatorial Pacific Ocean is due to the response of ultralong wave and long wave components of Rossby mode, and the EUP-like wave train crossing Eurasia is mainly due to the wave component of Rossby mode. (3) During northern winter, the warm water region in central equatorial Pacific Ocean is the source of forced wave trains. (4) In northern winter, the energy source for maintaining the short-term climatic oscillation is from the interaction between eddies, and between eddy and zonal flow.

A NUMERICAL STUDY OF SHORT-RANGE CLIMATIC OSCILLATION WITH VARIOUS TIME SCALES FORCED BY EL NINO DURING THE NORTHERN SUMMER

The normal mode method is adopted to decompose the differences between simulations with SST(sea surface temperature)anomahes over centra-eastern Pacific and normal SST by use of a nine-layer global spec- tral model in order to investigate short-range climatic oscillation with various time scales forced by El Nino during the northern summer.Investigation shows that El Nino may have the following influence on atmosphere on various space-time scales.Extra-long wave components of Rossby mode forced by convective anomaly over equatorial western Pacific resulting from El Nino produce climatic oscillation on monthly(sea- sonal)time scale in middle-high latitudes of Southern and Northern Hemispheres;extra-long wave components of Kelvin mode forced by SST anomalies propagate along the equator,resulting in 30—60 day oscillation of tropical and subtropical atmosphere;and its long waves move eastward with westerly,resulting in quasi-biweek oscillation.

Effects of Rotor Solidity on the Performance of Impulse Turbine for OWC Wave Energy Converter

Impulse turbine, working as a typical self-rectifying turbine, is recently utilized for the oscillating water column（OWC） wave energy converters, which can rotate in the same direction under the bi-directional air flows. A numerical model established in Fluent is validated by the corresponding experimental results. The flow fields, pressure distribution and dimensionless evaluating coefficients can be calculated and analyzed. Effects of the rotor solidity varying with the change of blade number are investigated and the suitable solidity value is recommended for different flow coefficients.

NUMERICAL STUDY OF QUASI-BIWEEKLY OSCILLATION IN TROPICAL ATMOSPHERE

By using a P-σ incorporated coordinate five-layer primitive equation spherical band model with surface temperature controlled by the heat balance equation,a simulation is done of disturbance formation in an anomalously warm SST area and of the quasi-biweekly oscillation(QBWO)of the disturbance,and associated rainfall and SST with SST being 1/3 period of oscillational phase ahead of rainfall.The study shows that the oscillation is produced by cloud-radiation interaction.Initial anomalously warm SST in the mid-western Pa- cific causes stronger oscillation than in the eastern.Hence the oscillation gets attenuated during the eastward movement of the disturbance.

A NUMERICAL STUDY ON THE INTERANNUAL TIME-SCALE LOW-FREQUENCY OSCILLATION

Low-frequency oscillation (LFO) of a large-scale flow pattern is an important observational characteristic feature. In this paper, under the forcing of annual periodic variation a two-layer quasi-geostrophic low- spectrum model is used for carrying out a prolonged numerical integration of more than 30 model years. In the model atmosphere, the interannual time-scale LFO is implicitly reproduced. The result is quite agreeable with the observational evidence.

Unsteady Flow Variability Driven by Rotor-stator Interaction at Rotor Exit

Numerical investigation of the unsteady flow variability driven by rotorstator interaction in a transonic axial compressor is performed. Two models with close and far axial gap between rotor and stator rows are studied in the simulation. Particular attention is attached to the analysis of mechanisms involved in driving rotor wake oscillation, rotor wake skewing and flow angle fluctuation at rotor exit. The results show that smaller axial gap is favorable to enhance the interaction in the region between two adjacent rows, and the fluctuation of the static pressure difference between two sides of rotor wake is improved by potential field from down stator, which is the driving force for rotor wake oscillation. The interaction between rotor and stator is weakened by increasing axial distance, rotor wake shifts to suction side of rotor blade with 5%-10% of rotor pitch, the absolute value of flow angle at rotor exit is less than that in the case of close interspace for every time step, and the fluctuation amplitude is also decreased.