Marine Ecosystem Dynamics Modeling Laboratory

Non-Hydrostatic Version of FVCOM

An effort has been made on upgrading FVCOM to a non-hydrostatic version to resolve vertical convection , internal waves, and small scale baroclinic instability. Two state-of-the-art approaches, projection method and pressure correction methods, were coded into FVCOM, with a fully-3D Poisson equation solver. Unlike other non-hydrostatic structured grid (Mahadevan et al. 1996; Marshall et al. 1997) and unstructured grid (Casulli and Stelling 1998 and Fringer et al. 2006), the non-hydrostatic version of FVCOM is solved using the same secon-order accurate finite-volume method with flexibility of using arbitrary triangular meshes (just like the hydrostatic version of FVCOM). The developmen is carried out by adding a core non-hydrostatic module in the current version of FVCOM, which allows users to make the model by selecting hydrostatic or non-hydrostatic version.

The non-hydrostatic module in FVCOM is coded and has been tested for selected idealized cases. A major step is to parallelize the matrix solver code of the non-hydrostatic pressure Poisson equation using PETSC (http://www.unix.mcs.anl.gov/petsc/petsc-as/).

Two examples for the validation experiments are listed in this website. For detailed information, please conduct Dr. Changsheng Chen or Dr. Geoffrey Cowles at SMAST/UMASSD

This work is accomplished by the Ph.D. graduate student Z. Lai under supervision of Dr. Chen and Dr. Cowles.

Validation Experiment 1: A Standing Surface Gravity Wave

A simple small-amplitude short surface gravity wave problem is set up to test the unstructured grid finite-volume non-hydrostatic algorithm and Possion equation solver in FVCOM. The analystical solution for a two-demensional, linear short surface gravity wave is given as

The numerical test was done using the 3-D code with assumption that all variables have no gradients in the y-direction. Both projection and pressure-correction methods were validated using this simple case and their solutions are identical.

A result can be viewed in an animation given here. In the animation, colors and contours present the non-hydrostatic pressure and free surface is amplified by a factor of 10 to provide a new view of the elevation change.

Click the play button or link to view the animation.

Validation Experiment 2: A Lock Exchange Experiment  

Lock exchange is a typical fluid dynamics problem to study density adjustment process at a discontinuous density interface. This problem has been widely used to validate a non-hydrostatic ocean model for its ability of resolving interface eddies and numerical stability. To test the second-order advection scheme and mass conservation nature of the finite-volume approached used in FVCOM, we set up this problem with no inclusion of any turbulence and molecular mixing.

Experiments were made for both projection and pressure correction methods. No significant difference was found in the results obtained from these two methods for both low and high-resolution cases, although the pressure-correction method is claimed to have a higher order accuracy than the projection method. Non-hydrostatic FVCOM can continue to run with no numerical instability problem.

We ran two cases with a density difference

An example is given here for an animation of the density evolution produced by the second case (with a large density difference).

Click the play button or link to view the animation.

Conditions: Non-hydrostatic, inviscous, two-dimensional, no extermal or internal forcing

Initial condition: velocity is zero everyhere and the domain is full of two homogeneous density water with a interface boundary at the middle point.

Posted on January 16, 2014