The PCH approach stores the conserved variables (mass, momentum, and total energy) at the node.
In this article, the convergence measure for reduction of remainder for such variables as momentum and mass was considered lower than 10−3, and for energy was considered 10−6.
The new approach stores the conserved variables (mass, momentum, and total energy) at the nodes of the mesh and solves the conservation equations on a control volume surrounding the point.
In a canonical description, one chooses a particular set of configuration variables xi and canonically conjugate momentum variables pi which describe the state of a system at some time, and can be encoded in a phase space.
We first use the ordered over-relaxation method to draw the momentum variable which could suppress the random walk behavior in Gibbs sampling stage.
For the discretisation with respect to the momentum variable, we employ spectrally convergent basis approximations using both Legendre polynomials and Gaussian radial basis functions.
Letting here p k = ∂ L ∂ q k ˙ ( q, q ˙ ), k = 1, 2 …, n. be the momentum variable, and using the transformation ( q, q ˙ ) = ( q, p ) we can write (13) as the Hamiltonian, H ( p, q, t ) = ∑ j = 1 n p j q ˙ j − L ( q, q ˙ ( q, p, t ), t ).
Here, y = u − α 2 u x x is a momentum variable, the constants α 2 and γ c 0 are squares of length scales, and c 0 = g h > 0 (where c 0 = 2 ω ) is the linear wave speed for undisturbed water at rest at spatial infinity, where h is the mean fluid depth and g is the gravitational constant.
Here, we used WEKA's default parameters, such as the learning rate = 0.3 and the momentum variable = 0.2.
