Search results for "numerical [Methods]"
showing 10 items of 500 documents
A NEW SOLVER FOR NON-ISOTHERMAL FLOWS IN NATURAL AND MIXED CONVECTION
2022
Most thermal fluid flow of real-life practical problems fall in the category of low Mach-number or incompressible flow (e.g., industrial flows inside ducts, or around stationary/moving objects, flows in biological/biomedical problems, or atmospheric flows). Several numerical techniques have been proposed for simulation of thermal flows, Finite Difference (FDM), Finite Element (FEM), Finite Volume (FVM) and Lattice Boltzmann (LBM) methods. Unlike the FVMs and FEMs, the classical FDMs show some difficulties in handling irregular geometries. Conventional formulation of FEMs (e.g., Galerkin FEMs) suffers from the lack of local mass balance, recovered by modified formulations (Narasimhan & W…
Contribution to the study and to the optimization of active thermographic process applied to surface crack detection
2017
The aim of this work is the detection of open and subjacent defects in metallic materials using laser-material interaction coupled with infrared thermography. This process is a possible alternative for magnetic particles testing and dye penetrant testing in the field of non-destructive testing. This work is divided into three main parties. At first, we have been interested in the characterization of optical and thermophysical properties of materials we used, in order to have good boundary conditions and also for the needs of temperatures fields measurements for validation. The second part concern the development of a numerical simulation model with two step approach: the first involves mode…
Efficiency and Stability of a Family of Iterative Schemes for Solving Nonlinear Equations
2019
In this paper, we construct a family of iterative methods with memory from one without memory, analyzing their convergence and stability. The main aim of this manuscript yields in the advantage that the use of real multidimensional dynamics gives us to decide among the different classes designed and, afterwards, to select its most stable members. Some numerical tests confirm the theoretical results.
Entropy dissipation of moving mesh adaptation
2014
Non-uniform grids and mesh adaptation have become an important part of numerical approximations of differential equations over the past decades. It has been experimentally noted that mesh adaptation leads not only to locally improved solution but also to numerical stability of the underlying method. In this paper we consider nonlinear conservation laws and provide a method to perform the analysis of the moving mesh adaptation method, including both the mesh reconstruction and evolution of the solution. We moreover employ this method to extract sufficient conditions — on the adaptation of the mesh — that stabilize a numerical scheme in the sense of the entropy dissipation.
MAST-2D diffusive model for flood prediction on domains with triangular Delaunay unstructured meshes
2011
Abstract A new methodology for the solution of the 2D diffusive shallow water equations over Delaunay unstructured triangular meshes is presented. Before developing the new algorithm, the following question is addressed: it is worth developing and using a simplified shallow water model, when well established algorithms for the solution of the complete one do exist? The governing Partial Differential Equations are discretized using a procedure similar to the linear conforming Finite Element Galerkin scheme, with a different flux formulation and a special flux treatment that requires Delaunay triangulation but entire solution monotonicity. A simple mesh adjustment is suggested, that attains t…
Verifications of Primal Energy Identities for Variational Problems with Obstacles
2018
We discuss error identities for two classes of free boundary problems generated by obstacles. The identities suggest true forms of the respective error measures which consist of two parts: standard energy norm and a certain nonlinear measure. The latter measure controls (in a weak sense) approximation of free boundaries. Numerical tests confirm sharpness of error identities and show that in different examples one or another part of the error measure may be dominant.
Solving the NLO BK equation in coordinate space
2015
We present results from a numerical solution of the next-to-leading order (NLO) Balitsky-Kovchegov (BK) equation in coordinate space in the large Nc limit. We show that the solution is not stable for initial conditions that are close to those used in phenomenological applications of the leading order equation. We identify the problematic terms in the NLO kernel as being related to large logarithms of a small parent dipole size, and also show that rewriting the equation in terms of the "conformal dipole" does not remove the problem. Our results qualitatively agree with expectations based on the behavior of the linear NLO BFKL equation.
Mirror and triplet displacement energies within nuclear DFT: : numerical stability
2017
Isospin-symmetry-violating class II and III contact terms are introduced into the Skyrme energy density functional to account for charge dependence of the strong nuclear interaction. The two new coupling constants are adjusted to available experimental data on triplet and mirror displacement energies, respectively. We present preliminary results of the fit, focusing on its numerical stability with respect to the basis size.
Mathematical and numerical analysis of initial boundary valueproblem for a linear nonlocal equation
2019
We propose and study a numerical scheme for bounded distributional solutions of the initial boundary value problem for the anomalous diffusion equation ∂t u +Lμu = 0 in a bounded domain supplemented with inhomogeneous boundary conditions. Here Lμ is a class of nonlocal operators including fractional Laplacian. ⃝c 2019 InternationalAssociation forMathematics andComputers in Simulation (IMACS). Published by ElsevierB.V.All rights reserved.
Numerically stable computation of step-sizes for descent methods. The nonconvex case
1977
The computation of step-sizes which guarantee convergence in unconstrained minimization by descent methods is considered. The use of a “control” or “range” function is highly attractive for this purpose because of its simplicity. Since the Armijo-Goldstein test may fail prematurely due to numerical instability near the minimizer, we consider a range function based on gradient values alone as has been done forg convex in [8]. Numerical algorithms are given for the computation of step-sizes whose behaviour under roundoff is shown to be benign in the sense of F. L. Bauer [5].