Taylor consistent discretisation of the Laplace operator in the Moving Particle Semi-implicit method

We derive a new Laplacian approximation for use in the Moving Particle Semi-Implicit method, ensuring a rigorous mathematical foundation based on Taylor expansion. The accuracy of this novel approximation is evaluated through comparison with other existing methods by studying the convergence rate of the numerical approximation in uniform and perturbed particle arrangements, and when solving a Poisson problem with different types of boundary conditions. The proposed model allows for easier implementation with respect to previous techniques, and always guarantees an accuracy of at least first order.