24. Guidelines for simulation setup

In this chapter, guidelines are given about how to choose values of the grid parameters and parameters that control the time step. Hereby, the focus is on the accurate simulation of waves.

24.1. Grid resolution and grid stretching

When a simulation of an undisturbed wave is performed, the rule is to use at least 60 cells per wavelength and at least 6 cells in the wave height. For higher waves, the number of cells in the wave height can be increased to (at least) 10. Note that as a consequence many cells are needed in the deeper part of the water, so some stretching may be applied in vertical direction, typically sz is between 1.01 and 1.03.

When an object is put into the wave and someone is interested in the local wave loads on the object, more cells are needed in the neighborhood of the object. There are two ways to take care of a fine grid near the object.

1. Use a small domain around the object (less than a wavelength) and simulate only a short time (one wave period or less). Then, a fine grid can be defined in this small domain. No stretching is needed, or only a very small level of stretching (sx,sy,sz \(\leq 1.01\)}). The central point of stretching should be placed at the point where the most interesting wave impact will occur. At the end of the domain, a Sommerfeld boundary condition or a simple Neumann condition (io=4 or io=2}, respectively) can be used, because reflections are less important when a short simulation time is used. In y-direction, solid walls are used, which are placed far enough from the object (typically 1 or 2 times the width on both sides of the object). In vertical direction, the total depth of the water can be taken, but for deep water, the domain can be cut off at about 2/3rd of the water depth.
2. When a longer simulation time is preferred, reflections against the outflow boundary require a careful choice of the domain length. Upon application of a GABC at the outflow boundary, the outflow can be chosen relatively close to the area of interest. It is also possible to use other outflow boundary conditions, but then a longer domain should be used. A damping zone can be added at the end of the domain, because the waves should be damped properly to prevent reflections. A a result the total domain (including a damping zone) is about two wave lengths or more. Take care that at least 60 cells per wavelength are used. In vertical direction, the total depth of the water can be taken, but in deep water, the domain can be cut off at about 2/3rd of the water depth.

When a grid study of a simulation is performed, the grid is mostly refined with a factor two each time. When a uniform grid is used, this is very easy, just increase imax, jmax and kmax with a factor 2 (or any factor you like). When a stretched grid is used (defined in ${INPUT}/comflow.in using parameters sx, sy and sz), special care has to be taken that grid refinement is done well. Not only imax, jmax and kmax have to be doubled, but also the stretch factors have to be adjusted. When the grid is refined with a factor two, the new stretch factors should have values of the square root of the old factors. For example: when using a grid of 30x30x30 grid points with sx=1.0, sy=1.0 and sz=1.0201, the refined grid should have values: 60x60x60 with sx=1.0, sy=1.0 and sz=1.01. In general, the value of sx^imax should remain constant for proper stretching in the x-direction.

24.2. Time integration and numerical stability

The time step is controlled during the run of the program using the following criteria:

• The time step of the very first cycle is given by the user in ${INPUT}/comflow.in. At the start of this first cycle, it is checked if this time step satisfies the diffusive restriction for the time step. If this criterion is not satisfied, the time step is adjusted.
• After the first cycle, the following criterion holds for changing the time step (if automatic time step adjustment is enabled): If the CFL number is larger than cflmax, the time step size is subsequently reduced by a factor of 2 in order to become smaller than cflmax again. If the CFL number is smaller than cflmin for a duration of at least 10 subsequent time steps the time is increased by a factor of 2 under the condition that the CFL number remains smaller than cflmax.

Hence, the time step can be controlled by the user by means of the parameters dtmax, cflmin and cflmax. When performing a wave simulation, there is a clear restriction of the time step for accuracy reasons. This restriction can be taken into account by setting dtmax=T/250, where T is the wave period.

For cflmin and cflmax the following must hold: 0< cflmin < cflmax <=1. The parameter cflmax is bounded by 1 to ensure stability, but for safety a smaller value should be taken. Useful values are cflmin=0.2 and cflmax=0.5 when the Forward Euler method is used. In case of Adams-Bashforth (see fixed_form_input/numerical) cflmin=0.04 and cflmax=0.1 is advised. When the influence of the time step is investigated, cflmin and cflmax can be used to tune the time step.