Pseudospectral element model for free surface viscous flows

Abstract

PurposeThe research is directed at development of an efficient and accurate technique for modelling incompressible free surface flows in which viscous effects may not be neglected. The paper describes the methodology, and gives illustrative results for simple geometries.Design/methodology/approachThe pseudospectral matrix element method of discretisation is selected as the basis for the CFD technique adopted, because of its high spectral accuracy. It is implemented as a means of solving the Navier‐Stokes equations coupled with the modified compressibility method.FindingsThe viscous solver has been validated for the benchmark cases of uniform flow past a cylinder at a Reynolds number of 40, and 2D cavity flows. Results for sloshing of a viscous fluid in a tank have been successfully compared with those from a linearised analytical solution. Application of the method is illustrated by the results for the interaction of an impulsive wave with a surface piercing circular cylinder in a cylindrical tank.Research limitations/implicationsThe paper demonstrates the viability of the approach adopted. The limitation of small amplitude waves should be tackled in future work.Practical implicationsThe results will have particular significance in the context of validating computations from more complex schemes applicable to arbitrary geometries.Originality/valueThe new methodology and results are of interest to the community of those developing numerical models of flow past marine structures.

A three-dimensional PSME model for rotating flows in an annular cavity

“…The two-stage technique is applied iteratively each time step until the absolute value of the first term in Equation (3) is less than the prescribed tolerance (see Chern et al, 2005 for more details).…”

“…Herein, Chebyshev polynomials are used for derivative expansions in the radial and the vertical directions and Fourier polynomials are used in the angular direction. This scheme is based on that of Chern et al (2001Chern et al ( , 2005. The domain is discretised according to the Chebyshev and Fourier collocation grid formulae as follows: Using equation (6), the collocation grid system is created in the physical domain.…”

A novel generalized diffusive SPH model: Theoretical analysis and 3D HPC implementation

“…In Fig. 6.2, the velocity field resulting from AQUAgpusph, at time instant t · U/L = 30, is compared with the streamlines obtained by Chern et al (2005). As it can be appreciated, a very good agreement exists between both solutions, with a small difference in the shape of the bottom vortexes.…”

“…6.2 Lid-driven cavity velocity field. Background streamlines obtained by Chern et al (2005). The arrows denote the velocity direction of each fluid particle, while the colour bar represents the normalized velocity module.…”

“…The lid-driven cavity flow has been widely applied in the past to verify CFD tools, becoming in fact a standard (see Ghia et al (1982), Ku et al (1987) and Chern et al (2005)). Moreover, it has been included in the set of SPHERIC validation tests.…”