Adaptive finite element analysis of free vibration of elastic membranes via element energy projection technique

Purpose A general strategy is developed for adaptive finite element (FE) analysis of free vibration of elastic membranes based on the element energy projection (EEP) technique. Design/methodology/approach By linearizing the free vibration problem of elastic membranes into a series of linear equivalent problems, reliable a posteriori point-wise error estimator is constructed via EEP super-convergent technique. Hierarchical local mesh refinement is incorporated to better deal with tough problems. Findings Several classical examples were analyzed, confirming the effectiveness of the EEP-based error estimation and overall adaptive procedure equipped with a local mesh refinement scheme. The computational results show that the adaptively-generated meshes reasonably catch the difficulties inherent in the problems and the procedure yields both eigenvalues with required accuracy and mode functions satisfying user-preset error tolerance in maximum norm. Originality/value By reasonable linearization, the linear-problem-based EEP technique is successfully transferred to two-dimensional eigenproblems with local mesh refinement incorporated to effectively and flexibly deal with singularity problems. The corresponding adaptive strategy can produce both eigenvalues with required accuracy and mode functions satisfying user-preset error tolerance in maximum norm and thus can be expected to apply to other types of eigenproblems.

Global storm tide modeling with ADCIRC v55: unstructured mesh design and performance

This paper details and tests numerical improvements to the ADvanced CIRCulation (ADCIRC) model, a widely used finite-element method shallow-water equation solver, to more accurately and efficiently model global storm tides with seamless local mesh refinement in storm landfall locations. The sensitivity to global unstructured mesh design was investigated using automatically generated triangular meshes with a global minimum element size (MinEle) that ranged from 1.5 to 6 km. We demonstrate that refining resolution based on topographic seabed gradients and employing a MinEle less than 3 km are important for the global accuracy of the simulated astronomical tide. Our recommended global mesh design (MinEle = 1.5 km) based on these results was locally refined down to two separate MinEle values (500 and 150 m) at the coastal landfall locations of two intense storms (Hurricane Katrina and Super Typhoon Haiyan) to demonstrate the model's capability for coastal storm tide simulations and to test the sensitivity to local mesh refinement. Simulated maximum storm tide elevations closely follow the lower envelope of observed high-water marks (HWMs) measured near the coast. In general, peak storm tide elevations along the open coast are decreased, and the timing of the peak occurs later with local coastal mesh refinement. However, this mesh refinement only has a significant positive impact on HWM errors in straits and inlets narrower than the MinEle and in bays and lakes separated from the ocean by these passages. Lastly, we demonstrate that the computational performance of the new numerical treatment is 1 to 2 orders of magnitude faster than studies using previous ADCIRC versions because gravity-wave-based stability constraints are removed, allowing for larger computational time steps.

A multilevel local mesh refinement with the PCD Method

We propose in this contribution a successive local mesh refinement with the PCD method. The multilevel local refinement improves the accuracy and gives a better precision, locally and globally, with a lower computational costs particularly if the considered problem has an anomaly. Here we present how a successive local mesh refinement can be handled. We conclude by presenting numerical experiments to show the interest of a multilevel local mesh refinement for the 2D diffusion equation.

A 3D Parallel High-Order Solver With Curved Local Mesh Refinement for Predicting Arterial Flow Through Varied Degrees of Stenoses

A 3D parallel high-order spectral difference (SD) solver with curved local mesh refinement is developed in this research to simulate flow through stenoses of varied degrees (50%, 60%, 65%, 70% and 75%) of radius constriction at inlet Reynolds number of 500. This solver employs high-order curved mesh in the vicinity of arterial wall and the local mesh refinement technique reduces the overall computational cost by distributing more elements in critical regions. In simulation of flow through stenosis of 50% radius constriction, velocity profiles predicted from the SD solver agree well with previous DNS results and experimental data. Mesh independency study shows that numerical results from a conforming and a non-conforming mesh agree well with each other. When the constriction degree is larger than 50%, visualizations through iso-surfaces of Q-criterion show that vortex rings are ejected from the stenosis throat, advecting downstream before they hit the vessel walls and they finally break down and merge into a large bulk region of small-scale turbulence. The observation is consistent with the vorticity contour which is characterized by development of the Kelvin-Helmholtz instability when shear layers are formed, rolled up and advected downstream between the central jet and the recirculation region. When the constriction degree turns to 75%, the flow transitions rapidly downstream of stenosis throat and dramatic pressure drop is witnessed. This provides a fluid-dynamic explanation for clinical definition of critical stenosis (i.e. over 75% luminal radius narrowing). Furthermore, pressure drop across a stenosis is found to be proportional to square of ratio of non-stenosed area to minimum area at the stenosis throat with a linear correlation coefficient equal to 0.9998. Finally, this solver is proven to have excellent scalability on massively parallel computers when multi-level refinement of meshes is performed to capture small-scale structures in the turbulence region.