A chemorepulsion model with superlinear production: analysis of the continuous problem and two approximately positive and energy-stable schemes

We consider the following repulsive-productive chemotaxis model: find u ≥ 0, the cell density, and v ≥ 0, the chemical concentration, satisfying $$ \left\{ \begin{array}{l} \partial_t u - {\Delta} u - \nabla\cdot (u\nabla v)=0 \ \ \text{ in}\ {\Omega},\ t>0,\\ \partial_t v - {\Delta} v + v = u^p \ \ { in}\ {\Omega},\ t>0, \end{array} \right. $$ ∂ t u − Δ u − ∇ ⋅ ( u ∇ v ) = 0 in Ω , t > 0 , ∂ t v − Δ v + v = u p i n Ω , t > 0 , with p ∈ (1, 2), ${\Omega }\subseteq \mathbb {R}^{d}$ Ω ⊆ ℝ d a bounded domain (d = 1, 2, 3), endowed with non-flux boundary conditions. By using a regularization technique, we prove the existence of global in time weak solutions of (1) which is regular and unique for d = 1, 2. Moreover, we propose two fully discrete Finite Element (FE) nonlinear schemes, the first one defined in the variables (u,v) under structured meshes, and the second one by using the auxiliary variable σ = ∇v and defined in general meshes. We prove some unconditional properties for both schemes, such as mass-conservation, solvability, energy-stability and approximated positivity. Finally, we compare the behavior of these schemes with respect to the classical FE backward Euler scheme throughout several numerical simulations and give some conclusions.

Numerical investigation of flow field around T-shaped spur dyke in a reverse-meandering channel

In this paper the flow characteristics near around T-shape spur dyke situated in reverse meandering channel having rigid bed is simulated using Renormalization Group (RNG) turbulence model with an ANSYS 2018 Fluent software. To solve the model in 3D ways we used Navier-Stroke's equation based on principle of conservation of mass and momentum within a moving fluid. For studying the flow characteristics, Computational Fluid Dynamics ware applied with all geometric parameter and the turbulence was simulated using (RNG) equations of model. In this simulation the structured meshes are used with different diameter and diameter of meshes is high at exit channel for obtaining accuracy in result. In this study we mainly focus on effect of Froude number on flow pattern and several other characteristics like velocity distribution, flow separation, bed shear stress distribution. The final result of this research work is compare with the condition when no structure is present in the channel.

GeoLinkage: a GRASS-GIS plugin to integrate surface waters and groundwater in WEAP-MODFLOW models

<p>Water resources management requires specialized computer tools that allow explicit integration of surface and groundwater fluxes, which generally have domains with different spatial discretization. On one hand, a surface hydrological domain, D1, is typically segmented in sub-basins, elevation contour bands or hydrological response units. These elements usually are represented by grids, triangles, or simple irregular polygons. In D1, the elements are connected to each other and incorporated into a drainage network that defines a surface topology, t1. On the other hand, an aquifer domain, D2, is organized in hydrogeological units, which can be represented by geometrical elements such as grids, triangulations, Voronoi or Quadratree diagrams. In D2, a regular connection is typically associated to structured meshes that defines a groundwater topology, t2. We present a new tool called GeoLinkage (v.geolinkage) that creates an ESRI-format linkage shapefile of the new surface-groundwater topology, t<sub>1-2</sub>. This python-based open-source tool has a graphical user interface (GUI) as an add-on for GRASS-GIS, which was constructed using Pygrass and Flopy libraries. It was developed to be used in WEAP-MODFLOV models, but it can also be used with other water resources management models. GeoLinkage allows processing models with reasonable computation times, which facilitates scenario analysis. It calculates the locations of the surface element geometries (nodes and arcs) using the GRASS platform and connects them to each element of a structured mesh in MODFLOW models. GeoLinkage was applied to obtain groundwater levels and coverage of water demand in Azapa Valley, a hyper-arid zone in the desert of Chile, where a grid of 70.305 cells and six fields with detailed geometry were processed in only 12 min.</p>

Deep action learning enables robust 3D segmentation of body organs in various CT and MRI images

In this study, we propose a novel point cloud based 3D registration and segmentation framework using reinforcement learning. An artificial agent, implemented as a distinct actor based on value networks, is trained to predict the optimal piece-wise linear transformation of a point cloud for the joint tasks of registration and segmentation. The actor network estimates a set of plausible actions and the value network aims to select the optimal action for the current observation. Point-wise features that comprise spatial positions (and surface normal vectors in the case of structured meshes), and their corresponding image features, are used to encode the observation and represent the underlying 3D volume. The actor and value networks are applied iteratively to estimate a sequence of transformations that enable accurate delineation of object boundaries. The proposed approach was extensively evaluated in both segmentation and registration tasks using a variety of challenging clinical datasets. Our method has fewer trainable parameters and lower computational complexity compared to the 3D U-Net, and it is independent of the volume resolution. We show that the proposed method is applicable to mono- and multi-modal segmentation tasks, achieving significant improvements over the state-of-the-art for the latter. The flexibility of the proposed framework is further demonstrated for a multi-modal registration application. As we learn to predict actions rather than a target, the proposed method is more robust compared to the 3D U-Net when dealing with previously unseen datasets, acquired using different protocols or modalities. As a result, the proposed method provides a promising multi-purpose segmentation and registration framework, particular in the context of image-guided interventions.

A New Method for Wet-Dry Front Treatment in Outburst Flood Simulation

When utilizing a finite volume method to predict outburst flood evolution in real geometry, the processing of wet-dry front and dry cells is an important step. In this paper, we propose a new approach to process wet-dry front and dry cells, including four steps: (1) estimating intercell properties; (2) modifying interface elevation; (3) calculating dry cell elevations by averaging intercell elevations; and (4) changing the value of the first term of slope limiter based on geometry in dry cells. The Harten, Lax, and van Leer with the contact wave restored (HLLC) scheme was implemented to calculate the flux. By combining the MUSCL (Monotone Upstream–centred Scheme for Conservation Laws)-Hancock method with the minmod slope limiter, we achieved second-order accuracy in space and time. This approach is able to keep the conservation property (C-property) and the mass conservation of complex bed geometry. The results of numerical tests in this study are consistent with experimental data, which verifies the effectiveness of the new approach. This method could be applied to acquire wetting and drying processes during flood evolution on structured meshes. Furthermore, a new settlement introduces few modification steps, so it could be easily applied to matrix calculations. The new method proposed in this study can facilitate the simulation of flood routing in real terrain.

Matrix equation solving of PDEs in polygonal domains using conformal mappings

We explore algebraic strategies for numerically solving linear elliptic partial differential equations in polygonal domains. To discretize the polygon by means of structured meshes, we employ Schwarz-Christoffel conformal mappings, leading to a multiterm linear equation possibly including Hadamard products of some of the terms. This new algebraic formulation allows us to clearly distinguish between the role of the discretized operators and that of the domain meshing. Various algebraic strategies are discussed for the solution of the resulting matrix equation.

Errors and uncertainties in simulation of steady, viscous flow past a circular cylinder at Re = 20 using a systematic approach

The use of Computational Fluid Dynamics as a tool for design and analysis of aerospace systems is well established. Since the results generated by a CFD solver are numerical approximations, the solution is inherently produced with errors and uncertainties. In this paper, a simple fluid flow problem of laminar, incompressible flow past a circular cylinder at Reynolds number of 20 is allowed to be solved by the well-known finite-volume solver ANSYS Fluent. The effect of variations in mesh resolution, domain boundary location and residual criteria settings is investigated. For all the cases, finite, structured meshes of acceptable quality are used. The influence of variables on the cylinder’s drag results is analyzed and discussed. An interesting pattern in results has been observed. The study on the variation in mesh resolution showed no presence of mesh independent solution. The study on the variation of the domain distance showed that it is necessary to increase the diameter of the circle several thousand times to obtain a domain independent solution.