Higher Resolution Hybrid-Upwind Spectral Finite-Volume Methods, for Flow in Porous and Fractured Media on Unstructured Grids

A novel higher resolution spectral volume method coupled with a control-volume distributed multi-Point flux approximation (CVD-MPFA) is presented on unstructured triangular grids for subsurface reservoir simulation. The flow equations involve an essentially hyperbolic convection equation coupled with an elliptic pressure equation resulting from Darcy’s law together with mass conservation. The spectral volume (SV) method is a locally conservative, efficient high-order finite volume method for convective flow. In 2D geometry, the triangular cell is subdivided into sub-cells, and the average state variables in the sub-cells are used to reconstruct a high-order polynomial in the triangular cell. The focus here is on an efficient strategy for reconstruction of both a higher resolution approximation of the convective transport flux and Darcy-flux approximation on sub-cell interfaces, which is also coupled with a discrete fracture model. The strategy involves coupling of the SV method and reconstructed CVD-MPFA fluxes at the faces of the spectral volume, to obtain an efficient finer scale higher resolution finite-volume method which solves for both the saturation and pressure. A limiting procedure based on a Barth-Jespersen type limiter is used to prevent non-physical oscillations on unstructured grids. The fine scale saturation/concentration field is then updated via the reconstructed finite volume approximation over the sub-cell control-volumes. Performance comparisons are presented for two phase flow problems on 2D unstructured meshes including fractures. The results demonstrate that the spectral-volume method achieves further enhanced resolution of flow and fronts in addition to that of achieved by the standard higher resolution method over first order upwind, while improving upon efficiency.

The Subcortical-Allocortical- Neocortical continuum for the Emergence and Morphological Heterogeneity of Pyramidal Neurons in the Human Brain

Human cortical and subcortical areas integrate emotion, memory, and cognition when interpreting various environmental stimuli for the elaboration of complex, evolved social behaviors. Pyramidal neurons occur in developed phylogenetic areas advancing along with the allocortex to represent 70–85% of the neocortical gray matter. Here, we illustrate and discuss morphological features of heterogeneous spiny pyramidal neurons emerging from specific amygdaloid nuclei, in CA3 and CA1 hippocampal regions, and in neocortical layers II/III and V of the anterolateral temporal lobe in humans. Three-dimensional images of Golgi-impregnated neurons were obtained using an algorithm for the visualization of the cell body, dendritic length, branching pattern, and pleomorphic dendritic spines, which are specialized plastic postsynaptic units for most excitatory inputs. We demonstrate the emergence and development of human pyramidal neurons in the cortical and basomedial (but not the medial, MeA) nuclei of the amygdala with cells showing a triangular cell body shape, basal branched dendrites, and a short apical shaft with proximal ramifications as “pyramidal-like” neurons. Basomedial neurons also have a long and distally ramified apical dendrite not oriented to the pial surface. These neurons are at the beginning of the allocortex and the limbic lobe. “Pyramidal-like” to “classic” pyramidal neurons with laminar organization advance from the CA3 to the CA1 hippocampal regions. These cells have basal and apical dendrites with specific receptive synaptic domains and several spines. Neocortical pyramidal neurons in layers II/III and V display heterogeneous dendritic branching patterns adapted to the space available and the afferent inputs of each brain area. Dendritic spines vary in their distribution, density, shapes, and sizes (classified as stubby/wide, thin, mushroom-like, ramified, transitional forms, “atypical” or complex forms, such as thorny excrescences in the MeA and CA3 hippocampal region). Spines were found isolated or intermingled, with evident particularities (e.g., an extraordinary density in long, deep CA1 pyramidal neurons), and some showing a spinule. We describe spiny pyramidal neurons considerably improving the connectional and processing complexity of the brain circuits. On the other hand, these cells have some vulnerabilities, as found in neurodegenerative Alzheimer’s disease and in temporal lobe epilepsy.

Form-Finding of Spine Inspired Biotensegrity Model

This paper presents a study on form-finding of four-stage class one self-equilibrated spine biotensegrity models. Advantageous features such as slenderness and natural curvature of the human spine, as well as the stabilizing network that consists of the spinal column and muscles, were modeled and incorporated in the mathematical formulation of the spine biotensegrity models. Form-finding analysis, which involved determination of independent self-equilibrium stress modes using generalized inverse and their linear combination, was carried out. Form-finding strategy for searching the self-equilibrated models was studied through two approaches: application of various combinations of (1) twist angles and (2) nodal coordinates. A total of three configurations of the spine biotensegrity models with different sizes of triangular cell were successfully established for the first time in this study. All members in the spine biotensegrity models satisfied the assumption of linear elastic material behavior. With the established spine biotensegrity model, the advantageous characteristics of flexibility and versatility of movement can be further studied for potential application in deployable structures and flexible arm in the robotic industry.

Six-Bar Linkages With Compliant Mechanisms for an Adaptive Robot

Programmable structures are formed by autonomous and adaptive triangular cells. However, they are composed of a large number of parts, specifically bearings, which make them laborious to manufacture and expensive. An essential part of these programmable structures are six-bar linkages, which allow to build cells that can preserve the underlying geometry of a triangular mesh. A major improvement, which is the main part of this paper, is to replace the joints of the six-bar-linkage by a compliant mechanism, which allows to manufacture them as one 3D printable part. A multibody system formulation is setup with the model of the compliant mechanisms, treating every joint either ideal or compliant with the given stiffness parameters. The multi-body formulation furthermore allows to include friction as well as an actuator model in a straight-forward manner. The overall stiffness parameter of the real system is then identified from a comparison with an experimental setup of a real compliant triangular cell. Finally, the model is used to show the deviations of a medium-scaled programmable structure with respect to the idealized behavior. The present paper marks a relevant step towards the realization of larger programmable structures as well as the development of 3D programmable structures.

FESOM-C v.2: coastal dynamics on hybrid unstructured meshes

We describe FESOM-C, the coastal branch of the Finite-volumE Sea ice – Ocean Model (FESOM2), which shares with FESOM2 many numerical aspects, in particular its finite-volume cell-vertex discretization. Its dynamical core differs in the implementation of time stepping, the use of a terrain-following vertical coordinate, and the formulation for hybrid meshes composed of triangles and quads. The first two distinctions were critical for coding FESOM-C as an independent branch. The hybrid mesh capability improves numerical efficiency, since quadrilateral cells have fewer edges than triangular cells. They do not suffer from spurious inertial modes of the triangular cell-vertex discretization and need less dissipation. The hybrid mesh capability allows one to use quasi-quadrilateral unstructured meshes, with triangular cells included only to join quadrilateral patches of different resolution or instead of strongly deformed quadrilateral cells. The description of the model numerical part is complemented by test cases illustrating the model performance.