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An outline of a time-domain boundary integral equation method (with second-order accuracy) for bodies floating on a fluid is given. It includes the full nonlinear dynamics of a potential flow with a free surface. To validate the method, a partially immersed body is forced to oscillate at a small amplitude for each of three modes. Relevant components of the reaction force on the body are integrated separately, thereby enhancing the accuracy of the hydrodynamic coefficients determined from this force signal. Linear frequency-domain results in a range of frequencies agree well with the present ones for the square, excellently for the circle. Nonlinear fluid-body interaction is simulated for a vertically oscillating square with amplitudes up to 80% of its draft. The force dependence on the motion amplitude provides a confirmation of second-order theory. Furthermore, the triple-frequency force component shows a pronounced cubic dependence on the amplitude.

We present Large Eddy Simulations of compressible turbulent flow within a finite volume approach with central spatial differencing. Different spatial discretisations yield quite different predictions of fluctuating flow properties although mean and integral flow properties appeared less sensitive. In the case of homogeneous, isotropic, decaying turbulence the Kolmogorov -(5/3) law is reproduced if the convective and viscous fluxes are treated with Simpson's cell vertex method. For the temporal flat plate exponentially growing unstable modes are recovered in the linear regime. Moreover, a scheme in which the viscous fluxes are treated with a 'vertex based' method is required in order to properly capture the saturation of growing fluctuations. due to nonlinear interactions.

A number of recent improvements in a higher-order three-dimensional (3D) panel method for highly nonlinear free surface wave simulations is discussed. Special attention is paid to grid evolution techniques, and stability of the time-dependent problem. Due to the improvements, stable and accurate results can be obtained for linear and highly nonlinear wave problems. Although no artificial smoothing is applied, even extreme problems like the development of breaking waves in a 3D configuration can be simulated. The computer code has been specially developed for implementation on a vector computer. The program is highly vectorized, and use is made of mathematical libraries for acceptable CPU-times.

The stationary electric field, current pattern and coupling losses in a multfilamentary, superconducting, twisted, torus-shaped wire are calculated for a torus placed in a homogeneous magnetic field increasing in time at a constant rate and parallel to the torus plane. The radius of the wire is considered to be small compared to the mean radius of the torus. An important parameter for the problem is the ratio between the twist length of the superconducting filaments and the mean radius of the torus. In the configuration considered this parameter is small. The coupling losses are approximately inversely proportional to the square of this ratio. Furthermore, for the wire to have unsaturated parts, the analysis shows that the rate of change of the magnetic field must decrease when this ratio increases.

Large eddy simulation of compressible, homogeneous, isotropic, decaying turbulence in a rectangular box is performed using finite volume techniques. An analysis of the energy spectra obtained from the simulations shows that an agreement with the Kolmogorov law for the inertial range is found only when an appropriate spatial discretization method is used. This agreement is obtained both for a low (0·05) and a moderate (0·6) Mach number when Smagorinsky's subgrid model is employed.

It is known that Harten's uniformly non-oscillatory scheme is a second-order accurate scheme for discretizing coservation laws. In this paper a multigrid technique and Runge-Kutta time stepping with frozen dissipation is applied to Harten's scheme in order to obtain the steady-state solution. It is shown that these techniques applied to Harten's scheme lead to a better convergence to the steady-state solution of a first-order conservation law than applied to Jameson's scheme.

Non-unique solutions to the Falkner-Skan equation with multiple inflection points have been investigated with respect to stability properties. A temporal stability analysis based on the Orr-Sommerfeld equation has been performed. Attention has been paid to the effect of the number of inflection points in these solutions on the stability properties. While the standard Falkner—Skan flow does not have any inflection points in a favourable pressure gradient, the first non–unique solution branch has two such points. The presence of these two inflection points implies a dramatic reduction of the critical Reynolds number by four orders of magnitude. Moreover, in base flows with more than two inflection points additional neutral waves occur with the same Reynolds number but with different wave numbers.

When I agreed to say something about Leen van Wijngaarden, I had forgotten how difficult such a task is. Especially when trying to do it in a language which is not one’s native tongue. The moment you start to reflect about it, a multitude of impressions, of characteristic gestures and attitudes come to mind, but the big question is how to catch these images in such words that the images come to life.

We have studied domain decomposition as a means to reduce the computational costs of the numerical simulation of propagating nonlinear water waves with a three-dimensional panel method. The iterative process of the domain decomposition method appeared to converge better than the corresponding two-dimensional method. In the application to a time-domain simulation it leads to a reduction of the computational requirements. However, due to the introduction of relatively more interface panels, reductions are not as large as in two dimensions.

We present a numerical method to investigate the stability of non-unique solutions of the Falkner-Skan equation

We present a higher order panel method for the numerical simulation of nonlinear gravity waves and ship motions in two and three dimensions. The method is based on a Green’s formulation for the velocity potential, which is introduced under the usual assumptions of an ideal fluid and an irrotational flow. Stable and accurate results for both linear and highly nonlinear waves are obtained. We discuss some essential feattires of our panel method, such as the time stepping mechanism and the approximation of the geometry. A variational formulation for the nonlinear free surface wave problem is presented, with direct implications for the numerical solution techniques which have been applied. Test results are shown for steady waves, overturning waves and wave-structure interactions. The numerical algorithm and preliminary results for surface piercing floating bodies are presented.

In this paper we discuss a higher order three dimensional panel method for nonlinear free surface wave simulations. A high degree of accuracy is obtained by a higher order resolution of the spatial problem and an efficient fourth order time integration method. Due to the accuracy, the algorithms provide stable results in the computation of linear and (highly) nonlinear wave problems.

In this article a review is given of analytical and numerical calculations on the electromagnetic properties of composite superconducting wires. The review is based on the research performed at the University of Twente during the last ten years. Due attention is given to related results in the literature.

It is known that Jameson's scheme is a pseudo-second-order-accurate scheme for solving discrete conservation laws. The scheme contains a non-linear artificial dissipative flux which is designed to capture shocks. In this paper, it is shown that the, shock-capturing of Jameson's scheme for the Euler equations can be improved by replacing the Lax-Friedrichs' type of dissipative flux with Roe's dissipative flux. This replacement is at a moderate expense of the calculation time.

We present an efficient higher order panel method for the numerical simulation of nonlinear gravity waves. The method is based on a Green’s formulation for the velocity potential that is introduced under the assumptions of an ideal fluid and an irrotational flow. This panel method gives accurate results for both linear and highly nonlinear waves. Test results are shown for a highly nonlinear Stokes wave and an overturning sinusoidal wave.

To compute the transient solution of free-surface flow problems in two and three dimensions boundary integral equation formulations are considered. Consistent lower and higher order approximations based on small curvature expansions are compared and applied to a time-dependent, linear free-surface wave problem.

The propeller blade is replaced by a source and doublet distribution referring to the acceleration potential. In the linearized approach used here, these distributions are situated at the helicoidal surface described by the propeller. The doublet distribution leads to a lifting surface problem, whereas the source distribution corresponds to a thickness problem for a usually nonsymmetrical blade. These problems can be solved independently. Results have been obtained for the pressure variations and for the noise level in certain points due to each of the two cases. It appears that the noise levels are of the same order of magnitude for the two cases. The essential step in the solution is the calculation of the field due to a source moving along a helicoidal line. This field has been obtained in the form of a parameter representation. The calculation of the field due to a doublet moving along a helicoidal line also has been performed.

Spectral methods can be adequate to solve problems in fluid dynamics numerically. A comprehensive treatment of these methods can be found in the book of Canuto, Hussaini, Quarteroni and Zang [1].

In this paper results are presented for three different time dependent problems. In the first place it is shown that the new stationary solutions as constructed in [4] and [5] are unstable.

Since the beginning of the seventies there is a growing interest in spectral methods as introduced by S.A. Orszag in 1970 [1]. Especially for problems with a high degree of continuity these methods can lead to very accurate results. In general problems are treated on simple geometries such as squares and boxes, either directly or by transformation of the region of interest.