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 here or images to view the full size flash 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.