Diagnosing numerical Cherenkov instabilities in relativistic plasma simulations based on general meshes

Numerical Cherenkov radiation (NCR) or instability is a detrimental effect frequently found in electromagnetic particle-in-cell (EM-PIC) simulations involving relativistic plasma beams. NCR is caused by spurious coupling between electromagnetic-field modes and multiple beam resonances. This coupling may result from the slow down of poorly-resolved waves due to numerical (grid) dispersion and from aliasing mechanisms. NCR has been studied in the past for finite-difference-based EM-PIC algorithms on regular (structured) meshes with rectangular elements. In this work, we extend the analysis of NCR to finite-element-based EM-PIC algorithms implemented on unstructured meshes. The influence of different mesh element shapes and mesh layouts on NCR is studied. Analytic predictions are compared against results from finite-element-based EM-PIC simulations of relativistic plasma beams on various mesh types.Comment: 31 pages, 20 figure

On the numerical modelling of bond for the failure analysis of reinforced concrete

The structural performance of reinforced concrete relies heavily on the bond between reinforcement and concrete. In nonlinear finite element analyses, bond is either modelled by merged, also called perfect bond, or coincident with slip, also called bond-slip, approaches. Here, the performance of these two approaches for the modelling of failure of reinforced concrete was investigated using a damage-plasticity constitutive model in LS-DYNA. Firstly, the influence of element size on the response of tension-stiffening analyses with the two modelling approaches was investigated. Then, the results of the two approaches were compared for plain and fibre reinforced tension stiffening and a drop weight impact test. It was shown that only the coincident with slip approach provided mesh insensitive results. However, both approaches were capable of reproducing the overall response of the experiments in the form of load and displacements satisfactorily for the meshes used

On the approximation in the smoothed finite element method (SFEM)

This letter aims at resolving the issues raised in the recent short communication [1] and answered by [2] by proposing a systematic approximation scheme based on non-mapped shape functions, which both allows to fully exploit the unique advantages of the smoothed finite element method (SFEM) [3, 4, 5, 6, 7, 8, 9] and resolve the existence, linearity and positivity deficiencies pointed out in [1]. We show that Wachspress interpolants [10] computed in the physical coordinate system are very well suited to the SFEM, especially when elements are heavily distorted (obtuse interior angles). The proposed approximation leads to results which are almost identical to those of the SFEM initially proposed in [3]. These results that the proposed approximation scheme forms a strong and rigorous basis for construction of smoothed finite element methods.Comment: 14 pages, 9 figures, 1 table; International Journal for Numerical Methods in Engineering, 201