An effective high-order element for analysis of two-dimensional linear problem using SBFEM

The scaled boundary finite element method (SBFEM) is a semi-analytical method, whose versatility, accuracy, and efficiency are not only equal to, but potentially better than the finite element method and the boundary element method for certain problems. This paper investigates the possibility of using an efficient high-order polynomial element in the SBFEM to form the approximation in the circumferential direction. The governing equations are formulated from the classical linear elasticity theory via the SBFEM technique. The scaled boundary finite element equations are formulated within a general framework integrating the influence of the distributed body source, mixed boundary conditions, contributions the side face with either prescribed surface load or prescribed displacement. The position of scaling center is considered for modeling problem. The proposed method is evaluated by solving two-dimensional linear problem. A selected set of results is reported to demonstrate the accuracy and convergence of the proposed method for solving problems in general boundary conditions.

A spectral multidomain penalty method solver for the numerical simulation of granular avalanches

This work presents a high-order element-based numerical simulation of an experimental granular avalanche, in order to assess the potential of these spectral techniques to handle conservation laws in geophysics. The spatial discretization of these equations was developed via the spectral multidomain penalty method (SMPM). The temporal terms were discretized using a strong-stability preserving Runge-Kutta method. Stability of the numerical scheme is ensured with the use of a spectral filter and a constant or regularized lateral earth pressure coefficient. The test case is a granular avalanche that is generated in a small-scale rectangular flume with topographical gradient. A grid independence test was performed to clarify the order of the error in the mass conservation produced by the treatments here implemented. The numerical predictions of the granular avalanches are compared with experimental measurements performed by Denlinger & Iverson (2001). Furthermore, the boundary conditions and parameters such as lateral earth pressure coefficients and the momentum correction factor were analyzed to observe the incidence of these features when solving the granular flow equations. This work identifies the benefits and weaknesses of the SMPM to solve this set of equations and, it is possible to conclude that the SMPM provides an appropriate solution of the granular flow equations proposed by Iverson & Denlinger (2001). Besides, it produces comparable predictions to experimental data and numerical results given by other schemes.