WAVETRISK-2.1: an adaptive dynamical core for ocean modelling

This paper introduces WAVETRISK-2.1 (i.e. WAVETRISK-OCEAN), an incompressible version of the atmosphere model wavetrisk-1.x with free-surface. This new model is built on the same wavelet-based dynamically adaptive core as wavetrisk, which itself uses DYNANICO's mimetic vector-invariant multilayer rotating shallow water formulation. Both codes use a Lagrangian vertical coordinate with conservative remapping. The ocean variant solves the incompressible multilayer shallow water equations with inhomogeneous density layers. Time integration uses barotropic--baroclinic mode splitting via an semi-implicit free surface formulation, which is about 34–44 times faster than an unsplit explicit time-stepping. The barotropic and baroclinic estimates of the free surface are reconciled at each time step using layer dilation. No slip boundary conditions at coastlines are approximated using volume penalization. The vertical eddy viscosity and diffusivity coefficients are computed from a closure model based on turbulent kinetic energy (TKE). Results are presented for a standard set of ocean model test cases adapted to the sphere (seamount, upwelling and baroclinic turbulence). An innovative feature of wavetrisk-ocean is that it could be coupled easily to the wavetrisk atmosphere model, thus providing a first building block toward an integrated Earth-system model using a consistent modelling framework with dynamic mesh adaptivity and mimetic properties.

A Refinement-by-Superposition Approach to Fully Anisotropic hp-Refinement for Improved Efficiency in CEM

We present an application of fully anisotropic hp-adaptivity over quadrilateral meshes for H(curl)-conforming discretizations in Computational Electromagnetics (CEM). Traditionally, anisotropic h-adaptivity has been difficult to implement under the constraints of the Continuous Galerkin Formulation; however, Refinement-by-Superposition (RBS) facilitates anisotropic mesh adaptivity with great ease. We present a general discussion of the theoretical considerations involved with implementing fully anisotropic hp-refinement, as well as an in-depth discussion of the practical considerations for 2-D FEM. Moreover, to demonstrate the benefits of both anisotropic h- and p-refinement, we study the 2-D Maxwell eigenvalue problem as a test case. The numerical results indicate that fully anisotropic refinement can provide significant gains in efficiency, even in the presence of singular behavior, substantially reducing the number of degrees of freedom required for the same accuracy with isotropic hp-refinement. This serves to bolster the relevance of RBS and full hp-adaptivity to a wide array of academic and industrial applications in CEM<br>

A Refinement-by-Superposition Approach to Fully Anisotropic hp-Refinement for Improved Efficiency in CEM

We present an application of fully anisotropic hp-adaptivity over quadrilateral meshes for H(curl)-conforming discretizations in Computational Electromagnetics (CEM). Traditionally, anisotropic h-adaptivity has been difficult to implement under the constraints of the Continuous Galerkin Formulation; however, Refinement-by-Superposition (RBS) facilitates anisotropic mesh adaptivity with great ease. We present a general discussion of the theoretical considerations involved with implementing fully anisotropic hp-refinement, as well as an in-depth discussion of the practical considerations for 2-D FEM. Moreover, to demonstrate the benefits of both anisotropic h- and p-refinement, we study the 2-D Maxwell eigenvalue problem as a test case. The numerical results indicate that fully anisotropic refinement can provide significant gains in efficiency, even in the presence of singular behavior, substantially reducing the number of degrees of freedom required for the same accuracy with isotropic hp-refinement. This serves to bolster the relevance of RBS and full hp-adaptivity to a wide array of academic and industrial applications in CEM<br>

Simulation of Slip-Oxidation Process by Mesh Adaptivity in a Cohesive Zone Framework

Adaptive oxide thickness was developed in a cohesive element based multi-physics model including a slip-oxidation and diffusion model. The model simulates the intergranular stress corrosion cracking (IGSCC) in boiling water reactors (BWR). The oxide thickness was derived from the slip-oxidation and updated in every structural iteration to fully couple the fracture properties of the cohesive element. The cyclic physics of the slip oxidation model was replicated. In the model, the thickness of the oxide was taken into consideration as the physical length of the cohesive element. The cyclic process was modelled with oxide film growth, oxide rupture, and re-passivation. The model results agreed with experiments in the literature for changes in stress intensity factor, yield stress representing cold work, and environmental factors such as conductivity and corrosion potential.

A quasi-monolithic phase-field description for mixed-mode fracture using predictor–corrector mesh adaptivity

In this work, we develop a mixed-mode phase-field fracture model employing a parallel-adaptive quasi-monolithic framework. In nature, failure of rocks and rock-like materials is usually accompanied by the propagation of mixed-mode fractures. To address this aspect, some recent studies have incorporated mixed-mode fracture propagation criteria to classical phase-field fracture models, and new energy splitting methods were proposed to split the total crack driving energy into mode-I and mode-II parts. As extension in this work, a splitting method for masonry-like materials is modified and incorporated into the mixed-mode phase-field fracture model. A robust, accurate and efficient parallel-adaptive quasi-monolithic framework serves as basis for the implementation of our new model. Three numerical tests are carried out, and the results of the new model are compared to those of existing models, demonstrating the numerical robustness and physical soundness of the new model. In total, six models are computationally analyzed and compared.

A mesh-independent framework for crack tracking in elastodamaging materials through the regularized extended finite element method

We propose a formulation for tracking general crack paths in elastodamaging materials without mesh adaptivity and broadening of the damage band. The idea is to treat in a unified way both the damaging process and the development of displacement discontinuities by means of the regularized finite element method. With respect to previous authors’ contributions, a novel damage evolution law and an original crack tracking framework are proposed. We face the issue of mesh objectivity through several two-dimensional tests, obtaining smooth crack paths and reliable structural results.

Polynomial spline spaces of non-uniform bi-degree on T-meshes: combinatorial bounds on the dimension

Polynomial splines are ubiquitous in the fields of computer-aided geometric design and computational analysis. Splines on T-meshes, especially, have the potential to be incredibly versatile since local mesh adaptivity enables efficient modeling and approximation of local features. Meaningful use of such splines for modeling and approximation requires the construction of a suitable spanning set of linearly independent splines, and a theoretical understanding of the spline space dimension can be a useful tool when assessing possible approaches for building such splines. Here, we provide such a tool. Focusing on T-meshes, we study the dimension of the space of bivariate polynomial splines, and we discuss the general setting where local mesh adaptivity is combined with local polynomial degree adaptivity. The latter allows for the flexibility of choosing non-uniform bi-degrees for the splines, i.e., different bi-degrees on different faces of the T-mesh. In particular, approaching the problem using tools from homological algebra, we generalize the framework and the discourse presented by Mourrain (Math. Comput. 83(286):847–871, 2014) for uniform bi-degree splines. We derive combinatorial lower and upper bounds on the spline space dimension and subsequently outline sufficient conditions for the bounds to coincide.