Non-singular Green's functions for the unbounded Poisson equation in one, two and three dimensions

This paper is a revised version of the original paper of same title--published in Applied Mathematics Letters 89--containing some corrections and clarifications to the original text. We derive non-singular Green's functions for the unbounded Poisson equation in one, two and three dimensions, using a cut-off function in the Fourier domain to impose a smallest length scale when deriving the Green's function. The resulting non-singular Green's functions are relevant to applications which are restricted to a minimum resolved length scale (e.g. a mesh size h) and thus cannot handle the singular Green's function of the continuous Poisson equation. We furthermore derive the gradient vector of the non-singular Green's function, as this is useful in applications where the Poisson equation represents potential functions of a vector field

High order Poisson Solver for unbounded flows

AbstractThis paper presents a high order method for solving the unbounded Poisson equation on a regular mesh using a Green's function solution. The high order convergence was achieved by formulating mollified integration kernels, that were derived from a filter regularisation of the solution field. The method was implemented on a rectangular domain using fast Fourier transforms (FFT) to increase computational efficiency. The Poisson solver was extended to directly solve the derivatives of the solution. This is achieved either by including the differential operator in the integration kernel or by performing the differentiation as a multiplication of the Fourier coefficients. In this way, differential operators such as the divergence or curl of the solution field could be solved to the same high order convergence without additional computational effort. The method was applied and validated using the equations of fluid mechanics as an example, but can be used in many physical problems to solve the Poisson equation on a rectangular unbounded domain. For the two-dimensional case we propose an infinitely smooth test function which allows for arbitrary high order convergence. Using Gaussian smoothing as regularisation we document an increased convergence rate up to tenth order. The method however, can easily be extended well beyond the tenth order. To show the full extend of the method we present the special case of a spectrally ideal regularisation of the velocity formulated integration kernel, which achieves an optimal rate of convergence

Numerical study of nominal wake fields of a container ship in oblique regular waves

Accurate estimation of the actual nominal wake behind the ship in waves is important for propeller designers when improving efficiency and minimizing cavitation. The present CFD study investigates the nominal wake fields of the Kriso Container Ship (KCS) in regular waves with wavelength equal to the ship length in five different headings. The ship is sailing at design speed and the wave steepness is 1/60. The results show that when sailing in the studied waves, the nominal wake fraction fluctuate up to 39% of the mean nominal wake fraction. The mean nominal wake fraction is higher than in calm water for all headings besides head sea waves. The maximum mean nominal wake fraction is found to occur in stern quartering sea waves, with a 16% higher mean nominal wake fraction than in calm water. It is also found that the transient bilge vortex and shadow from the skeg have a significant influence on the nominal wake field. Finally the study shows that the modified advance angle on the r/R=0.7 circle in the propeller plane varies 3.5 degrees more in port stern quartering than in calm water, increasing the risk of cavitation.ISSN:0141-118

CFD analysis of combustion and emission formation using URANS and LES under large two-stroke marine engine-like conditions

In this paper, the main aim is to examine the performance of turbulence models to shed light on the effect of turbulence modeling in capturing different in-cylinder phenomena under large two-stroke marine engine-like conditions. The Unsteady Reynolds Averaged Navier–Stokes (URANS) and Large Eddy Simulation (LES) turbulence models are utilized. The LES and URANS results are compared with experimental data, in which LES and URANS models show similar accuracy in capturing the pressure and heat release with a moderately better accuracy in the LES case. The predicted gas temperature at the liner wall is approximately 45% higher for URANS than LES during the expansion stroke, which may lead to different sulfuric acid formation and heat transfer prediction. The LES model predicts a 34% higher average swirl than that in the URANS case which leads to an earlier and a stronger interaction between the flame and the spray, decreasing the oxidation of the emissions. Due to the higher predicted in-cylinder temperature in the LES case, the NO emission amount at exhaust valve opening time (EVO) is 7% higher in the LES case. At EVO, the CO emission in the LES case is predicted to be 3-fold higher than that in the URANS case due to less oxidation of CO in the post oxidation stage in the LES case. The second cycle LES simulation shows that the solutions after the scavenging process are in-sensitive to the initial conditions.ISSN:1359-4311ISSN:1873-560

Hydrodynamics of Prey Capture and Transportation in Choanoflagellates

Choanoflagellates are unicellular microscopic organisms that are believed to be the closest living relatives of animals. They prey on bacteria through the act of the continuous beating of their flagellum, which generates a current through a crown-like filter. Subsequently, the filter retains bacterial particles from the suspension. The mechanism by which the prey is retained and transported along the filter remains unknown. We report here on the hydrodynamic effects on the transportability of bacterial prey of finite size using computational fluid dynamics. Here, the loricate choanoflagellate Diaphaoneca grandis serves as the model organism. The lorica is a basket-like structure found in only some of the species of choanoflagellates. We find that although transportation does not entirely rely on hydrodynamic forces, such forces positively contribute to the transportation of prey along the collar filter. The aiding effects are most possible in non-loricate choanoflagellate species, as compared to loricate species. As hydrodynamic effects are strongly linked to the beat and shape of the flagellum, our results indicate an alternative mechanism for prey transportation, especially in biological systems where having an active transport mechanism is costly or not feasible. This suggests an additional potential role for flagella in addition to providing propulsion and generating feeding currents.ISSN:2311-552