We demonstrate that the instabilities depend on the formulation of the nonlinear term.
An eigenvalue analysis of the fully discretized system shows that an instability is introduced by the formulation of the nonlinear term.
By introducing new formulations for the pressure gradient and a new formulation of the source term of the Poisson Pressure Equation (PPE), and by allowing a slight compressibility, we have proposed modified MPS methods for the prediction of wave impact pressure on a coastal structure.
By Taylor expanding Eq. (2), it can be shown that this formulation of the displacement term describes ballistic motion at short delay times, and diffusive motion at long delay times.
In our opinion this can be ascribed to the formulation of the questions; the term difficulty (translated in Dutch: 'moeite') may be not clear for some patients.
The mathematical formulation of the model terms and the combined model is validated using an in-house Fortran code.
The resulting spatial fluxes are similar to those derived using the so-called skew-symmetric formulation of the convective terms.
By doing this, the formulation of the source terms is unified leading to a single geometric source regarded as an apparent topography.
By means of numerical investigation we give evidence that these instabilities are related to the discontinuous Galerkin formulation of the velocity divergence term and the pressure gradient term that couple velocity and pressure.
