Interior Nodes Research Articles

Analysis of three-dimensional interior acoustic fields by using the localized method of fundamental solutions

• Applying the localized method of fundamental solutions for 3D interior acoustic fields. • The behavior of the present method for oscillating solution is first investigated. • Acoustic fields in a high-speed train and a room with complicated geometries are solved successfully. The traditional method of fundamental solutions has a full interpolation matrix, and thus its solution is computationally expensive, especially for large-scale problems with complicated domains. In this paper, we make a first attempt to apply the localized method of fundamental solutions for analysis of 3D interior acoustic fields. The present method first divides the whole computational domain into some overlapping subdomains, and then expresses physical variables as linear combinations of the fundamental solution in each subdomain. Finally, the method forms a sparse and banded system matrix by satisfying both governing equations at interior nodes and boundary conditions at boundary nodes. We provide four numerical experiments to verify the accuracy and the stability of the method. Comparisons of numerical results and computational time are also made between the present method, the method of fundamental solutions, and the COMSOL software.

Application of Lagrange Polynomial for Interpolating Income Generation from Certain Students’ Fee Structure

This paper presents the findings of the study that aimed to examine the changing aspects of income generation from certain students’ fee structure. It used an empirical example of Higher learning institution from Tanzania to determine whether Lagrange interpolation method would emerge a useful tool for interpolating and extrapolating enrolments of undergraduate students. The functional values evaluated at all nodes on the given data set accurately match the enrolments records of each respective academic year, though with nonconformities at the additional interior nodes. The function obtained from polynomial curve fitting using Excel spreadsheet at replaced the Lagrange polynomial to compute the rate of income generated from undergraduate students’ fees for academic years 2012/2013 to 2018/2019. The relative errors committed by range from the number at the node to the number at the node . Enrolments trend however is not stable, as it fluctuates basing on the particular academic year that causes the rate of income generated from undergraduate students’ fees to act wildly. Being the cause therefore oscillatory behaviour perhaps lax if enrolments grew continuously in the successive academic years, however, this would mark progressive manner if there will be reciprocal efforts to improve physical and electronic resources imbued by human resources capacity. Higher learning institutions could diversify their income generation strategies from multiplicity sources of incomes by using various techniques, including rising students’ fees and downhill expenses without compromising quality of services and products, reducing dependency on Government subsidies, and strengthening the rate of students’ retention in higher learning. They may also utilize to the maximum the unobserved multiplicity sources of incomes for instance; consultation fees, project funds, and new competitive learning programs to support realization of their strategic objectives in coherence with their missions and visions. Keywords: Enrolment, Generation, Income, Interpolation, Lagrange, Polynomial DOI : 10.7176/MTM/9-5-05 Publication date :May 31 st 2019

Extension of the local domain‐free discretization method to large eddy simulation of turbulent flows

SummaryIn this work, an immersed boundary method, called the local domain‐free discretization (DFD) method, is extended to large eddy simulation (LES) of turbulent flows. The discrete form of partial differential equations at an interior node may involve some nodes outside the solution domain. The flow variables at these exterior dependent nodes are evaluated via linear extrapolation along the direction normal to the wall. To alleviate the requirement of mesh resolution in the near‐wall region, a wall model based on the turbulence boundary layer equations is introduced. The wall shear stress yielded by the wall model and the no‐penetration condition are enforced at the immersed boundary to evaluate the velocity components at an exterior dependent node. For turbulence closure, a dynamic subgrid scale (SGS) model is adopted and the Lagrangian averaging procedure is used to compute the model coefficient. The SGS eddy viscosity at an exterior dependent node is set to be equal to that at the outer layer. To maintain the mass conservation near the immersed boundary, a mass source/sink term is added into the continuity equation. Numerical experiments on relatively coarse meshes with stationary or moving solid boundaries have been conducted to verify the ability of the present LES‐DFD method. The predicted results agree well with the published experimental or numerical data.

Localized method of fundamental solutions for solving two-dimensional Laplace and biharmonic equations

The localized method of fundamental solutions (LMFS) is proposed in this paper for solving two-dimensional boundary value problems, governed by Laplace and biharmonic equations, in complicated domains. Traditionally, the method of fundamental solutions (MFS) is a global method and the resultant matrix is dense and ill-conditioned. In this paper, it is the first time that the LMFS, the localized version of the MFS, is proposed. In the LMFS, the solutions at every interior node are expressed as linear combinations of solutions at some nearby nodes, while the numerical procedures of MFS are implemented within every local subdomain. The satisfactions of governing equation at interior nodes and boundary conditions at boundary nodes can yield a sparse system of linear algebraic equations, so the numerical solutions can be efficiently acquired by solving the resultant sparse system. Six numerical examples are given to demonstrate the effectiveness of the proposed LMFS.

Moving Finite Element Method-a Local Meshless Formulation

A novel discretization method is proposed and developed for numerical solution of boundary value problems governed by partial differential equations. In contrast to the standard Finite Element Method (FEM), the analyzed domain is not covered by a mesh of fixed non-overlapping finite elements, but only a net of nodes is used for discretization. Around each node, there is properly created a Lagrange finite element and the spatial variation of field variables is interpolated within this element in terms of nodal values and polynomial shape functions defined in the intrinsic coordinate space of the finite element. Thus, the Lagrange finite element associated with a node is moving within the analyzed domain from node to node. Since there are no element interfaces known in standard FEM with a fixed finite element mesh, there are eliminated the difficulties with continuity of derivatives of field variables on such interfaces and higher order derivatives are available within the moving finite element. This makes the Moving Finite Element (MFE) approximation to be applicable also to the development of the strong formulation of a boundary value problem with collocation of both the governing equations and boundary conditions at interior and boundary nodes, respectively. Besides the strong form also the local weak form can be developed with consideration of the governing equations in weak sense on local subdomains around each interior node. Since the local subdomain is involved inside the considered moving finite element, the MFE approximation is applicable to interpolation of field variables and their derivatives on local subdomain. The resulting system matrix of discretized equations is sparse. The reliability (accuracy and stability) and efficiency of the new method has been verified in numerical simulations for 2D problems of heat conduction in solids with possible continuous gradation of the heat conduction coefficient.

A NODE REGULATED DEFLECTION ROUTING SCHEME FOR CONTENTION MINIMZATION

Ponte Academic JournalNov 2019, Volume 75, Issue 11 A NODE REGULATED DEFLECTION ROUTING SCHEME FOR CONTENTION MINIMZATIONAuthor(s): Bakhe Nleya ,Andrew MutsvangwaJ. Ponte - Nov 2019 - Volume 75 - Issue 11 doi: 10.21506/j.ponte.2019.11.9 Abstract:The design and gradual deployment of all-optical\r\nbackbone network architectures will lead to the provisioning of\r\nenough bandwidth demands of future Internet of Things (IoT)�s\r\napplications and services. Current and future global traffic is increasingly\r\nbecoming heterogeneous as well as displaying structural\r\nself-similarity. Optical Burst Switching (OBS) is a practically\r\ncost-effective switching paradigm that can possibly address the\r\nmismatches between DWDM Terabit per second technology transmission\r\nspeeds and the required ultra-switching capabilities to\r\nserve the global traffic. Structurally, an OBS-switched backbone\r\nnetwork comprises buffered edge as well as bufferless core (interior)\r\nnodes. Because of the bufferless nature of the interior nodes,\r\nthe core of such networks tends to be quite prone to frequent contention\r\noccurrences that can easily cause significant overall network\r\nperformance degradation due to sporadic heavy burst loses.\r\nSuch drawbacks can be partly countered by appropriately dimensioning\r\navailable network resources, and reactively by way of deflecting\r\nexcess as well as contending traffic to available alternate\r\npaths. In doing so, diverted traffic must not trigger network performance\r\ndegradation in the deflection paths. Because minimizing\r\ncontentions is key to provisioning a consistent quality of service\r\n(QoS), we thus in this paper propose and analyze a scheme that\r\nseeks to intelligently deflect traffic in the core network such that\r\nQoS degradations caused by contention occurrences are negligible.\r\nSince contention minimization will lead to improved overall\r\nnetwork performance, we herein propose a regulated deflection\r\nrouting scheme (rDr) that utilizes neural network agents to reinforce\r\nthe deflection routing decisions at core nodes. The scheme is\r\nevaluated by way of simulations and results show that it can minimize\r\nburst loses as well as keep end-to-end delays for the various\r\napplications to within acceptable bounds. It also significantly reduces\r\nthe frequency of contention occurrences as well as burst deflections. Download full text:Check if you have access through your login credentials or your institution Username Password

Lattice Boltzmann method for conjugated heat and mass transfer with general interfacial conditions

A general interfacial treatment for the transport process in multicomponent systems governed by the convection-diffusion equation, together with conjugated interfaces where continuity or discontinuity interfacial conditions with regard to the physical scalar and its flux exist, is developed using the lattice Boltzmann method (LBM) with a multiple-relaxation-time collision operator. Factors accounting for interfacial jumps at conjugated interfaces typically include the difference in solubility, porosity, and transport properties, and the interfacial transport resistance. Difficulties in satisfying the discontinuity conditions, where continuity conditions are inherent in the conventional LBM, are overcome based on a second-order accurate treatment for both Dirichlet and Neumann boundary conditions. As a result, the unknown populations at the interface are obtained with a combination of the existing postcollision populations and the defined interfacial jumps without finite-difference approximations, thereby enabling the interfacial requirements precisely. Since the present treatment considers local intersected link fractions of the interface, it can be applied for curved interfaces naturally. As for straight interfaces located at the midpoints of the nodes, the present treatment can be significantly simplified with only two current nodes required. Validation work on the present treatment are performed with four specific problems, including the steady and unsteady convection diffusion in a fluid-fluid channel, steady convection diffusion in a fluid-solid system, steady and unsteady pure conduction in a composite slab, and steady pure conduction in an annulus. Such an interfacial scheme is finally applied to the conjugated mass transfer in a heterogonous medium, highlighting its practicability in complex systems with complicated interfacial conditions. In addition, detailed error analysis on interior nodes, interfacial values, and interfacial fluxes shows that our model is second-order accurate in space for straight interfaces regardless of various interfacial conditions, indicating no artificial disturbance is introduced to the model. While for curved interface, only superlinear and first-order accuracies are obtained for the interior nodes and the interfacial values or fluxes, respectively. Discussions on the degradation of the accuracy are presented. Note that the present interfacial treatment is mainly focused on two-dimensional problems, extensions of the model to be three-dimensional are straightforward.

Imposition of boundary conditions for elliptic equations in the context of non boundary fitted meshless methods

This paper describes a novel method to treat Neumann and Dirichlet boundary conditions in meshless discretizations of elliptic equations using nodal integration. The usual meshless framework for boundary fitted discretizations is first presented. Then, the possibility of dealing with non boundary fitted clouds of points is integrated into this framework. With this new method, the discretization of the boundary can automatically be generated from a covering point cloud in such a fashion that the degrees of freedom of the final discrete problem are associated with interior nodes only. This process minimally depends on the description of the simulation domain as it only needs to test whether a point is inside or outside of the domain. The emphasis is strongly set on building an adequate discrete structure, which allows a convenient interpretation of necessary conditions to pass the linear patch test.

Ontogeny and phylogeny of the cercopithecine cranium: A geometric morphometric approach to comparing shape change trajectories

While the analysis of ontogenetic trajectories is common in geometric morphometrics (GM), the simultaneous comparison of several trajectories can be unwieldy and is, in some cases, unable to make use of one of the main advantages of GM, visualization. Furthermore, due to the paucity of the paleontological record, analyses of trajectories are often limited to extant taxa. We address these issues by presenting a method for visualizing the similarities and differences of cranial ontogenetic trajectories among taxa and a method for reconstructing ancestral ontogenetic trajectories, so that these differences can be investigated in a phylogenetic context. We also tested for the presence of phylogenetic signal in the ontogenetic trajectories themselves. Using an ontogenetic series of 522 crania, representing 17 cercopithecine species from 8 genera, we first calculated ontogenetic trajectories of cranial shape change for each species, and then entered these trajectories into a principal components analysis to produce a developmental shape-change trajectory PCA (δPCA). Then, through an augmentation of the phylomorphospace approach, we projected a molecular phylogeny onto the major axes of trajectory shape variation from the δPCA to produce an ‘ontophylomorphospace,’ using squared-change parsimony to reconstruct interior nodes. Through these procedures, we were able to determine that the δPCAs illustrate patterns of variation in these developmental trajectories in a visually intuitive manner that allows for easier comparisons among taxa. Through examination of the ontophylomorphospace, we found that African papionins exhibit extensive homoplasy in the evolution of cranial ontogenetic trajectories, and that Asian species of Macaca show highly derived ontogenetic trajectories relative to other cercopithecines. Additionally, we found no support for the presence of a phylogenetic signal in cranial ontogenetic trajectories. The δPCA and the ontophylomorphospace are ways in which to visualize and compare complex, multivariate shape transformations, both among extant taxa and over evolutionary time, respectively.

Stability of an explicit high‐order spectral element method for acoustics in heterogeneous media based on local element stability criteria

SummaryThis paper considers the stability of an explicit leapfrog time marching scheme for the simulation of acoustic wave propagation in heterogeneous media with high‐order spectral elements. The global stability criterion is taken as a minimum over local element stability criteria, obtained through the solution of element‐borne eigenvalue problems. First, an explicit stability criterion is obtained for the particular case of a strongly heterogeneous and/or rapidly fluctuating medium using asymptotic analysis. This criterion is only dependent upon the maximum velocity at the vertices of the mesh elements, and not on the velocity at the interior nodes of the high‐order elements. Second, in a more general setting, bounds are derived using statistics of the coefficients of the elemental dispersion matrices. Different bounds are presented, discussed, and compared. Several numerical experiments show the accuracy of the proposed criteria in one‐dimensional test cases as well as in more realistic large‐scale three‐dimensional problems.

CWBound: boundary node detection algorithm for complex non-convex mobile ad hoc networks

Efficient message forwarding in mobile ad hoc network in disaster scenarios is challenging because location information on the boundary and interior nodes is often unavailable. Information related to boundary nodes can be used to design efficient routing protocols as well as to prolong the battery power of devices along the boundary of an ad hoc network. In this article, we developed an algorithm, CWBound, which discovers boundary nodes in a complex non-convex mobile ad hoc (CNCAH) networks. Experiments show that the CWBound algorithm is at least three times faster than other state-of-the-art algorithms, and up to 400 times faster than classical force-directed algorithms. The experiments also confirmed that the CWBound algorithm achieved the highest accuracy (above 97% for 3 out of the 4 types of CNCAH networks) and sensitivity (90%) among the algorithms evaluated.

On the optimal tuning and placement of FEC codecs within multicasting trees for resilient publish/subscribe services in edge-IoT architectures

Publish/subscribe services represent the key choice to glue together the huge amount of heterogeneous devices available within the Internet of Things, by making them interoperable at a large scale through mediation systems and facilities available in the cloud. In such a scenario, several optimizations have been introduced in the architectural layout by pushing parts of the service intelligence away from centralized points to the logical extremes, namely the edge, of the infrastructure, according to the edge computing paradigm. Such services can establish tree-based overlays among the involved nodes, and are used on top of unreliable networks, where packets have a non-negligible probability to be lost. In order to reduce such losses affecting wide area communications, the need to move data towards the cloud has been reduced by placing more frequent computations at the edge of the infrastructure, nearer to data sources, according to the edge computing paradigm. However, this is not enough and, in order to provide resilient and reliable communications, publish/subscribe implementations have been equipped with means to achieve loss-tolerance, which unfortunately have been proved to be ineffective (by lacking having end-to-end guarantees) and inefficient (by compromising the communication performance). In this paper, we identify Forward Error Correction as a suitable method to have efficient and effective loss tolerance within multicast trees, and describe how dealing with its issues by having the interior nodes within the multicast trees to generate spatial redundancy in addition to the one produced by the root. The decision of which nodes on the network edge must generate the additional redundancy and how many additional packets must be forwarded has been approached by using a Single-Leader Multi-Follower Game. Such an approach has been empirically assessed and compared with a centralized one, represented by a genetic algorithm, and with gossiping, so as to show the achievement of optimal decisions.

An inverse three spectra problem for Sturm\u2013Liouville operators

In this paper, we consider the inverse three spectra problems of recovering the Sturm–Liouville equation by the spectra of the Neumann–Dirichlet boundary value problem on [0,1], the Neumann–Robin problem on [0,1/2], and the Robin–Dirichlet problem on [1/2,1], where the two Robin parameters at the interior node x=1/2 are considered to be different. The algorithm of construction is presented and sufficient conditions for three sequences to be the spectral data of the mentioned boundary problems are given.

The coalescent of a sample from a binary branching process

At time 0, start a time-continuous binary branching process, where particles give birth to a single particle independently (at a possibly time-dependent rate) and die independently (at a possibly time-dependent and age-dependent rate). A particular case is the classical birth–death process. Stop this process at time T>0. It is known that the tree spanned by the N tips alive at time T of the tree thus obtained (called a reduced tree or coalescent tree) is a coalescent point process (CPP), which basically means that the depths of interior nodes are independent and identically distributed (iid). Now select each of the N tips independently with probability y (Bernoulli sample). It is known that the tree generated by the selected tips, which we will call the Bernoulli sampled CPP, is again a CPP. Now instead, select exactly k tips uniformly at random among the N tips (a k-sample). We show that the tree generated by the selected tips is a mixture of Bernoulli sampled CPPs with the same parent CPP, over some explicit distribution of the sampling probability y. An immediate consequence is that the genealogy of a k-sample can be obtained by the realization of k random variables, first the random sampling probability Y and then the k−1 node depths which are iid conditional on Y=y.

Flexible colour patterns obscure identification and mimicry in Indo-Pacific Chromodoris nudibranchs (Gastropoda: Chromodorididae)

Chromodoris is a genus of colourful nudibranchs that feed on sponges and is found across the Indo-Pacific. While this was once the most diverse chromodorid genus, recent work has shown that the genus should be restricted to a monophyletic lineage that contains only 22 species, all of which exhibit black pigmentation and planar spawning behaviour. Earlier phylogenies of this group are poorly resolved and thus additional work is needed to clarify species boundaries within Chromodoris. This study presents a maximum-likelihood phylogeny based on mitochondrial loci (COI, 16S) for 345 Chromodoris specimens, including data from 323 new specimens and 22 from GenBank, from across the Indo-Pacific. Species hypotheses and phylogenetic analysis uncovered 39 taxa in total containing 18 undescribed species, with only five of 39 taxa showing stable colour patterns and distinct morphotypes. This study also presents the first evidence for regional mimicry in this genus, with C. colemani and C. joshi displaying geographically-based variation in colour patterns which appear to match locally abundant congenerics, highlighting the flexibility of these colour patterns in Chromodoris nudibranchs. The current phylogeny contains short branch lengths, polytomies and poor support at interior nodes, which is indicative of a recent radiation. As such, future work will employ a transcriptome-based exon capture approach for resolving the phylogeny of this group. In all, this study included 21 of the 22 described species in the Chromodoris sensu stricto group with broad sampling coverage from across the Indo-Pacific, constituting the most comprehensive sampling of this group to date. This work highlights several cases of undocumented diversity, ultimately expanding our knowledge of species boundaries in this group, while also demonstrating the limitations of colour patterns for species identification in this genus.

An immersed boundary/wall modeling method for RANS simulation of compressible turbulent flows

SummaryIn this paper, an immersed boundary (IB) method is developed to simulate compressible turbulent flows governed by the Reynolds‐averaged Navier‐Stokes equations. The flow variables at the IB nodes (interior nodes in the immediate vicinity of the solid wall) are evaluated via linear interpolation in the normal direction to close the discrete form of the governing equations. An adaptive wall function and a 2‐layer wall model are introduced to reduce the near‐wall mesh density required by the high resolution of the turbulent boundary layers. The wall shear stress modified by the wall modeling technique and the no‐penetration condition are enforced to evaluate the velocity at an IB node. The pressure and temperature at an IB node are obtained via the local simplified momentum equation and the Crocco‐Busemann relation, respectively. The SST k − ω and S‐A turbulence models are adopted in the framework of the present IB approach. For the Shear‐Stress Transport (SST) k − ω model, analytical solutions in near‐wall region are utilized to enforce the boundary conditions of the turbulence equations and evaluate the turbulence variables at an IB node. For the S‐A model, the turbulence variable at an IB node is calculated by using the near‐wall profile of the eddy viscosity. In order to validate the present IB approach, numerical experiments for compressible turbulent flows over stationary and moving bodies have been performed. The predictions show good agreements with the referenced experimental data and numerical results.

Finit element solution of Poisson Equation over Polygonal Domains using a novel auto mesh generation technique and an explicit integration scheme for linear convex quadrilaterals of cubic order Serendipity and Lagrange families

This paper presents an explicit integration scheme to compute the stiffness matrix of twelve node and sixteen node linear convex quadrilateral finite elements of Serendipity and Lagrange families using an explicit integration scheme and discretisation of polygonal domain by such finite elements using a novel auto mesh generation technique, In finite element analysis, the boundary value problems governed by second order linear partial differential equations, the element stiffness matrices are expressed as integrals of the product of global derivatives over the linear convex quadrilateral region. These matrices can be shown to depend on the material properties matrices and the matrix of integrals with integrands as rational functions with polynomial numerator and the linear denominator (4+) in the bivariates over a 2-square (-1 ) with the nodes on the boundary and in the interior of this simple domain. The finite elements up to cubic order have nodes only on the boundary for Serendipity family and the finite elements with boundary as well as some interior nodes belong to the Lagrange family. The first order element is the bilinear convex quadrilateral finite element which is an exception and it belongs to both the families. We have for the present ,the cubic order finite elements which havee 12 boundary nodes at the nodal coordinates {(-1,-1),(1,-1),(1,1),(-1,1),(-1/3,-1), (1/3,-1),(1,-1/3),(1,1/3),(1/3,1),(-1/3,1),(-1,1/3),(-1,-1/3)} and the four interoior nodal coordinates at the points (-1/3,-1/3),(1/3,-1/3),(1/3,1/3),(-1/3,1/3)} in the local parametric space ( In this paper, we have computed the integrals of local derivative products with linear denominator (4+) in exact forms using the symbolic mathematics capabilities of MATLAB. The proposed explicit finite element integration scheme can be then applied to solve boundary value problems in continuum mechanics over convex polygonal domains. We have also developed a novel auto mesh generation technique of all 12-node and 16-node linear(straight edge) convex quadrilaterals for a polygonal domain which provides the nodal coordinates and the element connectivity. We have used the explicit integration scheme and this novel auto mesh generation technique to solve the Poisson equation u ,where u is an unknown physical variable and in with Dirichlet boundary conditions over the convex polygonal domain.

GPU-based detection of protein cavities using Gaussian surfaces

BackgroundProtein cavities play a key role in biomolecular recognition and function, particularly in protein-ligand interactions, as usual in drug discovery and design. Grid-based cavity detection methods aim at finding cavities as aggregates of grid nodes outside the molecule, under the condition that such cavities are bracketed by nodes on the molecule surface along a set of directions (not necessarily aligned with coordinate axes). Therefore, these methods are sensitive to scanning directions, a problem that we call cavity ground-and-walls ambiguity, i.e., they depend on the position and orientation of the protein in the discretized domain. Also, it is hard to distinguish grid nodes belonging to protein cavities amongst all those outside the protein, a problem that we call cavity ceiling ambiguity.ResultsWe solve those two ambiguity problems using two implicit isosurfaces of the protein, the protein surface itself (called inner isosurface) that excludes all its interior nodes from any cavity, and the outer isosurface that excludes most of its exterior nodes from any cavity. Summing up, the cavities are formed from nodes located between these two isosurfaces. It is worth noting that these two surfaces do not need to be evaluated (i.e., sampled), triangulated, and rendered on the screen to find the cavities in between; their defining analytic functions are enough to determine which grid nodes are in the empty space between them.ConclusionThis article introduces a novel geometric algorithm to detect cavities on the protein surface that takes advantage of the real analytic functions describing two Gaussian surfaces of a given protein.

Exterior foam drainage and flow regime switch in the foams

The three-dimensional flow in exterior microscale foams including the Plateau borders and nodes are investigated by solving Navier-stoke and continuity equations. First, we show the effect of the interfacial mobility and film thickness on the dimensionless mean velocity of the exterior foams. The velocity of the exterior node-PB is similar to the velocity of single exterior Plateau border. Next, we calculated the pressure difference of each element separately and obtained their hydraulic resistances. We found out that the hydraulic resistance of the exterior Plateau border is always larger than the hydraulic resistance of the exterior node, resulting in a consistent channel-dominated regime. However, For the interior foams, there is a value of interfacial mobility where the node’s resistance overcomes the channel’s resistance, resulting in a switch from the channel-dominated regime to a node-dominated regime. This switching point is dependent on the relative length of the channels. Hence, we obtained an approximation of the interfacial mobility switching points versus the relative length of channels. Moreover, in a form of approximation master curve, we showed the dependence of mean velocities of foams and channels’ hydraulic resistances to a dimensionless combined parameter of Λ-1 that contains interfacial mobility and film thickness together. For both the exterior and interior nodes, the velocity and hydraulic resistance are almost constant for various Boussinesq numbers since interfacial mobility has a marginal effect on node’s flow.

Strong-form approach to elasticity: Hybrid finite difference-meshless collocation method (FDMCM)

• FDMCM combines the finite difference and the strong form meshless method. • FDMCM scheme uses a uniform Cartesian grid embedded in complex geometry. • The method is suited for problems with geometries known imperfectly from images. • FDMCM method combines the advantages of both FD and meshless methods. We propose a numerical method that combines the finite difference (FD) and strong form (collocation) meshless method (MM) for solving linear elasticity equations. We call this new method FDMCM. The FDMCM scheme uses a uniform Cartesian grid embedded in complex geometries and applies both methods to calculate spatial derivatives. The spatial domain is represented by a set of nodes categorized as (i) boundary and near boundary nodes, and (ii) interior nodes. For boundary and near boundary nodes, where the finite difference stencil cannot be defined, the Discretization Corrected Particle Strength Exchange (DC PSE) scheme is used for derivative evaluation, while for interior nodes standard second order finite differences are used. FDMCM method combines the advantages of both FD and DC PSE methods. It supports a fast and simple generation of grids and provides convergence rates comparable to weak formulations. We demonstrate the appropriateness and robustness of the proposed scheme through various benchmark problems in 2D and 3D. Numerical results show good accuracy and h -convergence properties. The ease of computational grid generation makes the method particularly suited for problems where geometries are very complicated and known only imperfectly from images, frequently occurring in e.g. geomechanics and patient-specific biomechanics, where the proposed FDMCM method, after its extension to non-linear regime, appears to be a promising alternative to the traditional weak form-based numerical schemes used in the field.