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A Level-set Algorithm for Simulating Wildfire Spread
Get PDFLevel-set approaches are efficient and versatile methods for solving interface tracking problems and have been used in recent years to describe wildland fire propagation. Being based on an Eulerian description of the spread problem, their numerical implementation offers improved computational agility and better portability to parallel computing environments with respect to vector-based simulators. The use of a continuous representation of the fire perimeter in place of the binary formulation used in Cellular Automata avoids the commonly observed distortion of the fire shape. This work presents an algorithm for fire-spread simulation based on a level-set formulation. The results are compared to the ones obtained by two well-known Cellular Automata simulators under homogeneous conditions, and to the ones given by a well-know vector-based fire-spread simulator under realistic slope and wind conditions. According to this work, the level-set approach provides better results, in terms of accuracy, at a much reduced computational cost
Collocation Methods to Solve Certain Hilbert Integral Equation with Middle Rectangle Rule
Get PDFThe generalized composite middle rectangle rule for the computation of Hilbert integral is discussed. The pointwise superconvergence phenomenon is presented, i.e., when the singular point coincides with some a priori known point, the convergence rate of the rectangle rule is higher than what is global possible. We proved that the superconvergence rate of the composite middle rectangle rule occurs at certain local coordinate of each subinterval and the corresponding superconvergence error estimate is obtained. By choosing the superconvergence point as the collocation points, a collocation scheme for solving the relevant Hilbert integral equation is presented and an error estimate is established. At last, some numerical examples are provided to validate the theoretical analysis
Free-Space Fundamental Solution of a 2D Steady Slow Viscous MHD Flow
Get PDFThe fundamental free-space 2D steady creeping MHD flow produced by a concentrated point force of strength g located at a so-called source point x0 in an unbounded conducting Newtonian liquid with uniform viscosity µ and conductivity σ > 0 subject to a prescribed uniform ambient magnetic field B = Be1 is analytically obtained. More precisely, not only the produced flow pressure p and velocity u but also the resulting stress tensor field σ are expressed at any observation point x ≠ x0 in terms of usual modified Bessel functions, the vectors g, x-x0 and the so-called Hartmann layer thickness d = (√µ/σ)/B (see Hartmann (1937)). The resulting basic flows obtained for g either parallel with or normal to the magnetic field B are examined and found to exhibit quite different properties
Non Probabilistic Solution of Fuzzy Fractional Fornberg-Whitham Equation
Get PDFFractional Fornberg-Whitham equation has a vast application in physics. There exist various investigations for the above problem by considering the variables and parameters as crisp/exact. In practice, we may not have these parameters exactly but those may be known in some uncertain form. In the present paper, these uncertainties are taken as interval/fuzzy and the authors proposed here a new method viz. that of the double parametric form of fuzzy numbers to handle the uncertain fractional Fornberg-Whitham equation. Using the single parametric form of fuzzy numbers, original fuzzy fractional Fornberg-Whitham equation is converted first to an interval based fuzzy differential equation. Next this equation is transformed to crisp form by applying the proposed double parametric form of fuzzy numbers. Finally it has been solved using homotopy perturbation method (HPM). Present method performs very well in terms of computational efficiency. The reliability of the method is shown by obtaining an approximate numerical solution for different cases. Results are given in term of plots and are also compared in special cases
Bäcklund Transformations: a Link Between Diffusion Models and Hydrodynamic Equations
Get PDFThis work presents a new analytical method to transform exact solutions of linear diffusion equations into exact ones for nonlinear advection-diffusion models. The proposed formulation, based on Bäcklund transformations, is employed to obtain velocity fields for the unsteady two-dimensional Helmholtz equation, starting from analytical solutions of a heat conduction type model
Vertical Vibrations of an Elastic Foundation with Arbitrary Embedment within a Transversely Isotropic, Layered Soil
Get PDFThis paper introduces a numerical model to investigate the vibratory response of elastic and rigid circular plates embedded in viscoelastic, transversely isotropic, three-dimensional layered media. In the present numerical scheme, the boundary-value problem corresponding to the case of time-harmonic concentrated and distributed axisymmetric vertical ring loads within a layered half-space is formulated according to an exact stiffness method. Its solution results in the required influence functions for the modeling of the present problem. The case of an embedded flexible plate is formulated in terms of a variational method. The deflection profile of the plate is written in terms of generalized coordinates combined with a polynomial approximation. These generalized coordinates are determined by the solution of the Lagrange's equation of motion, which involves the strain and kinetic energy of the flexible plate and energy due to contact tractions, as well as the potential energy due to the applied load. A set of Lagrange multipliers is incorporated into the equation of motion so that the boundary conditions at the plate edge are satisfied. The solution of the constrained Lagrangian function results in the deflection profile of the plate. The deflection profile of the embedded plate is shown for different governing parameters such as frequency and type of excitation and layering configuration of the surrounding medium. The present numerical scheme contributes to the study of dynamic response of buried foundations and anchors in non-homogeneous soils
Composite Simpson’s Rule for Computing Supersingular Integral on Circle
Get PDFThe computation with Simpson’s rule for the supersingular integrals on circle is discussed. When the singular point coincides with some priori known point, the convergence rate of the Simpson rule is higher than the globally one which is considered as the superconvergence phenomenon. Then the error functional of density function is derived and the superconvergence phenomenon of composite Simpson rule occurs at certain local coordinate of each subinterval. Based on the error functional, a modify quadrature is presented. At last, numerical examples are provided to validate the theoretical analysis and show the efficiency of the algorithms
Multiscale Modeling of Collagen Fibril in Bone at Various Crosslink Densities: An Insight into Its Deformation Mechanisms
Get PDFMultiscale modeling of collagen fibril is carried out by incorporating the material properties of collagen obtained from steered molecular dynamics into the finite element model of collagen fibril with inclusion of crosslinks. The results indicate that the nonbonded interactions between collagen and mineral contribute to the significant enhancement of the elastic modulus of collagen fibril at all the crosslink densities in both the low strain and high strain regimes. The crosslinks are found to play an important role in the mechanical response of collagen fibril, the enhancement in elastic modulus ranging from 5-11% for various crosslink densities compared to the collagen fibril with no crosslinks. Further, two different mechanisms of fibril deformation are described based on the characteristic length of collagen fibril. The deformation mechanism is governed by the pullout between the ends of collagen molecules in the overlap zone, following the breaking of crosslinks, if the effective length is greater than the characteristic length. However, if the effective length is less than the characteristic length the deformation mechanism is influenced by the shearing between the staggered collagen molecules which are adjacent to each other
Molecular Dynamics Simulations of Ions Diffusion in Carbon Nanotubes Embedded in Cell Membrane
Get PDFIn this paper, we present molecular dynamics simulations of diffusion of Na+, K+, and Cl- ions through the single-walled carbon nanotubes(SWCNTs) that are embedded into the membrane of cells in aqueous solutions. A simplified atomic cell model that considers bilayer membranes is employed to study the transportation of ions inside CNTs. The simulated results indicate that the diffusion properties of ions and selectivity of CNT with respect to ions are affected by biological complexity of the cell membrane. We have found that the ion diffusion only occurs in the CNTs with chirality higher than (8, 8), which is bigger than the result without membranes (7, 7) and different ions have different critical diameters. Moreover, the CNT inserted into membrane showed selective ability to K+ against Na+, which is in agreement with the selectivity for bio-channels
Variable Viscosity and Density Biofilm Simulations using an Immersed Boundary Method, Part I: Numerical Scheme and Convergence Results
Get PDFThe overall goal of this work is to develop a numerical simulation which correctly describes a bacterial biofilm fluid-structure interaction and separation process. In this, the first of a two-part effort, we fully develop a convergent scheme and provide numerical evidence for the method order as well as a full 3D separation simulation. We use an immersed boundary-based method (IBM) to model and simulate a biofilm with density and viscosity values different from than that of the surrounding fluid. The simulation also includes breakable springs connecting the bacteria in the biofilm which allows the inclusion of erosion and detachment into the simulation. We use the incompressible Navier-Stokes (N-S) equations to describe the motion of the flowing fluid and discretize the fluid equations using finite differences. We use a geometric multigrid method to solve the resulting equations at each time step. We note that the use of multigrid is necessary because of the dramatically different densities and viscosities between the biofilm and the surrounding fluid. We investigate and simulate the model in both two and three dimensions.
We also note that our method differs from several previous attempts of using IBM for modeling biofilm/flow interactions in the following ways: the density and viscosity of the biofilm can differ substantially from the surrounding fluid, and the Lagrangian node locations correspond to experimentally measured bacterial cell locations from 3D images taken of Staphylococcus epidermidis in a biofilm. In the followup article, we will present the results of the validation of this model and calibration to several experimental scenarios