Abstract
A meshless numerical model is developed to simulate single-phase, Newtonian, compressible flow in the Cartesian coordinate system. The coupled set of partial differential equations, i.e., ...mass conservation, momentum conservation, energy conservation, and equation of state is solved by using Diffuse Approximate Method (DAM) and Pressure Implicit with Splitting of Operators (PISO) pressure correction algorithm on an irregular node arrangement. DAM is structured by using the second-order polynomial basis functions and the Gaussian weight function, leading to the weighted least squares approximation on overlapping sub-domains. Implicit time discretization is performed for the predictor step of PISO, while in the corrector steps the equations are discretized explicitly. The numerical model is validated for flow between parallel plates with helium obeying ideal gas law. The solver’s accuracy is assessed by investigating the shape of the Gaussian weight and the number of the nodes in the local subdomains. The calculated velocity, temperature and pressure fields are compared with the Finite Volume Method (FVM) results obtained by OpenFOAM software and show a reasonably good agreement.
Abstract The interface between two immiscible Newtonian liquids with different densities and the same viscosity, influenced by gravity, is based on the Phase-Field Method (PFM) formulation. The ...solution of the related governing coupled Navier-Stokes (NS) and Cahn-Hillard (CH) equations is structured by the meshless Diffuse Approximate Method (DAM) and Pressure Implicit with Splitting of Operators (PISO). The variable density is involved in the inertial and buoyancy terms (non-Boussinesq formulation). The related moving boundary problem is handled through single-domain, irregular, fixed node arrangement in two-dimensional Cartesian coordinates. The meshless DAM uses weighted least squares approximation on overlapping subdomains, polynomial shape functions of second-order and Gaussian weights. Implicit time discretisation is performed for the NS and CH equations in the momentum predictor and Phase-Field (PF) variable corrector steps of PISO, while the momentum corrector steps solve the NS equation explicitly. This solution procedure has improved stability compared to Chorin’s pressure-velocity coupling, previously used in meshless solutions of related problems. The Rayleigh-Taylor instability problem simulations are performed for an Atwood number of 0.76. The DAM parameters (shape parameter of the Gaussian weight function and number of nodes in a local subdomain) are the same as in the author’s previous studies on single-phase flows. The simulations did not need any upwinding in the range of the simulations. The results compare well with the mesh-based finite volume method studies performed with the open-source code Gerris.
Abstract Dendritic morphology is one of the most common microstructures in solidifying metallic materials. The phase-field method represents one of the most suitable approaches for modelling the ...evolution of dendritic morphology. In this paper, the meshless RBF-FD method and forward Euler scheme are used to solve the partial differential equations arising from the phase-field model for dendritic growth. We consider the growth of a single dendrite into a supercooled pure melt. On the computational domain’s surfaces, we apply symmetric boundary conditions. Special care has to be taken in the RBF-FD method to satisfy boundary conditions accurately. In this paper, we test four different implementations of boundary conditions. In the first one, the boundary conditions are incorporated when constructing an interpolation problem in local support domains containing boundary nodes. In the second one, the interpolation problem in the local support domains does not consider boundary conditions, which are satisfied by solving a system of linear equations for values in all boundary nodes at each time step. The third one complements the second one with the use of ghost nodes. The fourth implementation is an alternative one, where the values in ghost nodes are determined by direct mirroring. The accuracy and computational efficiency of all four implementations are compared. We discuss the advantages and disadvantages of each implementation. We show that using ghost nodes is recommended for implementing Neumann boundary conditions in the RBF-FD method.
The intense shipping traffic characterising the Adriatic Sea favours the spread of marine organisms. Yet, a study of 12 Adriatic ports (4 on the western side and 8 on the eastern side of the basin) ...found that non-indigenous species (NIS) accounted for only 4% of the benthic communities settled on hard substrates. The cirripeds Amphibalanus amphitrite and Balanus trigonus, found in 8 harbours, were the most common invaders followed by Amphibalanus eburneus, the ascidian Styela plicata, and the bivalve Magallana gigas. The highest percentage of NIS was recorded in Venice and Ploče, the harbours with the least rich native communities; the lowest percentage was retrieved in Trieste, Koper, Pula, and Rijeka, the harbours hosting the highest species diversity. In contrast, the ports of Bari and Ancona showed both high NIS percentages and highly diversified communities.
•Harbours represent a suitable receptacle for non-indigenous species (NIS).•Fouling macrobiota were investigated from twelve western and eastern Adriatic ports.•Highest percentages of NIS were obtained where total Richness was low.•Biotic and abiotic factors are crucial in defining the vulnerability to invasibility.
A novel numerical procedure is developed for modelling two-dimensional dendritic solidification in dilute binary alloys. The evolution of the phases and the solute concentration is described by the ...partial differential equations, obtained from the phase field model. The meshless radial basis function-generated finite difference (RBF-FD) method is used for the spatial discretisation of the partial differential equations. The forward Euler scheme is used for the time-stepping. In order to reduce the computational cost, an adaptive procedure is developed, based on the quad-tree strategy, ensuring the highest density of the computational nodes at the solid-liquid interface. In the procedure, the computational domain is divided into overlapping sub-domains which can be dynamically refined or coarsened. The regular or scattered node distribution with constant node density is used for discretisation of each sub-domain. The h-adaptive procedure is ensured by the constant product between the area of a sub-domain and the computational node density. The accuracy and speedup in comparison to the solution on a uniform node distribution are assessed by solving the benchmark problem for dendritic solidification in dilute binary alloys. The main originality of the model represents the first use of RBF-FD method for the spatial discretisation of the PF equations in combination with adaptive solution procedure. The RBF-FD method can be used on unstructured node distributions, which is especially advantageous in the solution of PF model for dendritic growth, since the solution is very sensitive to the regularity of the node distribution. The developed spatial-temporal-adaptive numerical model represents an accurate and computationally efficient tool for the prediction of the dendrite morphology and micro-segregation during the solidification in binary alloys.
Abstract
We have developed a 2-D numerical meshless adaptive approach for phase-field modelling of dendritic solidification. The quadtree-based approach decomposes the computational domain into ...quadtree sub-domains of different sizes. The algorithm generates uniformly-distributed computational nodes in each quadtree sub-domain. We apply the meshless radial basis function generated finite difference method and the forward Euler scheme to discretise governing equations in each computational node. The fixed ratio between the characteristic size and the node spacing of a quadtree sub-domain ensures space adaptivity. The adaptive time-stepping accelerates the calculations further. In the framework of previous research studies, we used the approach to solve quantitative phase-field models for single dendrite growth in pure melts and dilute binary alloys. In the present study, we upgrade the solution procedure for the modelling growth of multiple differently oriented dendrites. Along with the space-time adaptive approach, we apply non-linear preconditioning of the phase-field equation to increase computational efficiency. We investigate a novel numerical approach’s accuracy and computational efficiency by simulating the equiaxed dendrite growth from a dilute binary alloy.
The present paper is a contribution to the first initiative of the Port Baseline Survey (PBS) for Non-indigenous species (NIS) in the Mediterranean Sea. It presents a report on the soft-bottom ...macrobenthos from the five Adriatic ports: Bari, Ancona (Italy), Koper (Slovenia), Pula, Rijeka (Croatia), with a focus on the presence and contribution of NIS to native assemblages. Out of 451 species identified, only four were common to all ports. A total of eight NIS were recorded, five in surveyed ports and three in the lagoon connected to the Port of Koper. The highest number of NIS was recorded in Bari, and the highest abundance in Ancona and Bari. Generally, the number, abundance and contribution of NIS seems too low to cause a substantial impact on native communities in surveyed ports. The suitability of methods adopted for PBS for soft-bottom NIS was discussed and suggestion for methodological improvement is provided.
•Soft-bottom macrobenthos were investigated from five Adriatic ports.•Contribution of Non-indigenous species (NIS) to native assemblages was discussed.•Contribution of NIS seems too low to cause a substantial impact on native communities.•The suitability of methods adopted for Port Baseline Survey for soft-bottom NIS was discussed.•Suggestions for methodological improvement are provided.
The travelling slice approximation of continuous casting process is widely used in industrial practice to model the heat transfer and solidification. Short computational times that are possible due ...to the reduction from three to two dimensions compensate for lower accuracy introduced by the approximation. In the same spirit, the travelling slice approximation is also used for the thermomechanical model in the present paper. The model includes contributions from metallostatic pressure, thermal contraction and viscoplastic deformation to describe the stress in the material slice. It incorporates simple models to predict the hot tearing and cracking. The model is solved with a novel strong-form meshless method. It allows flexible adaptive node distribution to accurately describe the behaviour in the solidifying region. In this paper we focus on the two-way coupling of the heat transfer and deformation of the strand to model the air-gap formation in the initial stage of the casting process and to study the emergent behaviour that is the result of this coupling. We find that the inclusion of the air-gap model significantly changes the stress distribution in the corners of the strand because of the reheating caused by the reduced heat-transfer.
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