Search results for "Numerical"
showing 10 items of 2002 documents
High Order Extrapolation Techniques for WENO Finite-Difference Schemes Applied to NACA Airfoil Profiles
2017
Finite-difference WENO schemes are capable of approximating accurately and efficiently weak solutions of hyperbolic conservation laws. In this context high order numerical boundary conditions have been proven to increase significantly the resolution of the numerical solutions. In this paper a finite-difference WENO scheme is combined with a high order boundary extrapolation technique at ghost cells to solve problems involving NACA airfoil profiles. The results obtained are comparable with those obtained through other techniques involving unstructured meshes.
On the hyperbolicity of certain models of polydisperse sedimentation
2012
The sedimentation of a polydisperse suspension of small spherical particles dispersed in a viscous fluid, where particles belong to N species differing in size, can be described by a strongly coupled system of N scalar, nonlinear first-order conservation laws for the evolution of the volume fractions. The hyperbolicity of this system is a property of theoretical importance because it limits the range of validity of the model and is of practical interest for the implementation of numerical methods. The present work, which extends the results of R. Burger, R. Donat, P. Mulet, and C.A. Vega (SIAM Journal on Applied Mathematics 2010; 70:2186–2213), is focused on the fluxes corresponding to the …
Approximate Lax–Wendroff discontinuous Galerkin methods for hyperbolic conservation laws
2017
Abstract The Lax–Wendroff time discretization is an alternative method to the popular total variation diminishing Runge–Kutta time discretization of discontinuous Galerkin schemes for the numerical solution of hyperbolic conservation laws. The resulting fully discrete schemes are known as LWDG and RKDG methods, respectively. Although LWDG methods are in general more compact and efficient than RKDG methods of comparable order of accuracy, the formulation of LWDG methods involves the successive computation of exact flux derivatives. This procedure allows one to construct schemes of arbitrary formal order of accuracy in space and time. A new approximation procedure avoids the computation of ex…
Flotation with sedimentation: Steady states and numerical simulation of transient operation
2020
Abstract A spatially one-dimensional model of the hydrodynamics of a flotation column is based on one continuous phase, the fluid, and two disperse phases: the aggregates, that is, bubbles with attached hydrophobic valuable particles, and the solid particles that form the gangue. A common feed inlet for slurry mixture and gas is considered and the bubbles are assumed to be fully aggregated with hydrophobic particles as they enter the column. The conservation law of the three phases yields a model expressed as a system of partial differential equations where the nonlinear constitutive flux functions come from the drift-flux and solids-flux theories. In addition, the total flux functions are …
A system of conservation laws with discontinuous flux modelling flotation with sedimentation
2019
Abstract The continuous unit operation of flotation is extensively used in mineral processing, wastewater treatment and other applications for selectively separating hydrophobic particles (or droplets) from hydrophilic ones, where both are suspended in a viscous fluid. Within a flotation column, the hydrophobic particles are attached to gas bubbles that are injected and float as aggregates forming a foam or froth at the top that is skimmed. The hydrophilic particles sediment and are discharged at the bottom. The hydrodynamics of a flotation column is described in simplified form by studying three phases, namely the fluid, the aggregates and solid particles, in one space dimension. The relat…
The exact finite‐difference scheme for vector boundary‐value problems with piece‐wise constant coefficients
1998
We will consider the exact finite‐difference scheme for solving the system of differential equations of second order with piece‐wise constant coefficients. It is well‐known, that the presence of large parameters at first order derivatives or small parameters at second order derivatives in the system of hydrodynamics and magnetohydrodynamics (MHD) equations (large Reynolds, Hartmann and others numbers) causes additional difficulties for the applications of general classical numerical methods. Thus, important to work out special methods of solution, the so‐called uniform converging computational methods. This gives a basis for the development of special monotone finite vector‐difference schem…
SSPMO: A Scatter Tabu Search Procedure for Non-Linear Multiobjective Optimization
2007
We describe the development and testing of a metaheuristic procedure, based on the scatter-search methodology, for the problem of approximating the efficient frontier of nonlinear multiobjective optimization problems with continuous variables. Recent applications of scatter search have shown its merit as a global optimization technique for single-objective problems. However, the application of scatter search to multiobjective optimization problems has not been fully explored in the literature. We test the proposed procedure on a suite of problems that have been used extensively in multiobjective optimization. Additional tests are performed on instances that are an extension of those consid…
A new approximation procedure for fractals
2003
AbstractThis paper is based upon Hutchinson's theory of generating fractals as fixed points of a finite set of contractions, when considering this finite set of contractions as a contractive set-valued map.We approximate the fractal using some preselected parameters and we obtain formulae describing the “distance” between the “exact fractal” and the “approximate fractal” in terms of the preselected parameters. Some examples and also computation programs are given, showing how our procedure works.
On the numerical solution of some finite-dimensional bifurcation problems
1981
We consider numerical methods for solving finite-dimensional bifurcation problems. This paper includes the case of branching from the trivial solution at simple and multiple eigenvalues and perturbed bifurcation at simple eigenvalues. As a numerical example we treat a special rod buckling problem, where the boundary value problem is discretized by the shooting method.
Looking More Closely at the Rabinovich-Fabrikant System
2016
Recently, we looked more closely into the Rabinovich–Fabrikant system, after a decade of study [Danca & Chen, 2004], discovering some new characteristics such as cycling chaos, transient chaos, chaotic hidden attractors and a new kind of saddle-like attractor. In addition to extensive and accurate numerical analysis, on the assumptive existence of heteroclinic orbits, we provide a few of their approximations.