The present work proposes the extension of the IMERSPEC methodology for numerical simulations of two-phase flows. This methodology consists of the fusion between the Fourier pseudospectral method and the immersed boun...
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ISBN:
(纸本)9783319198002;9783319197999
The present work proposes the extension of the IMERSPEC methodology for numerical simulations of two-phase flows. This methodology consists of the fusion between the Fourier pseudospectral method and the immersed boundary method for non-periodical problems. This method was originally developed for single-phase and incompressible flows (Mariano et al., Comput Model Eng Sci 59: 181-216, 2010). In the present paper, we extend this methodology for two-phase flows using the front-tracking method to model the fluid-fluid interface. The results involving the spurious currents, mass conservation and analysis through numerical experimental bubbles rise, show that the proposed method can be considered validated and promising to computational fluid dynamics (CFD).
In this work we consider a coupled system of m(>= 2) linear singularly perturbed equations of reaction-diffusion type coupled in the reaction terms with discontinuous source term. The leading term of each equation ...
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ISBN:
(纸本)9783319257273;9783319257259
In this work we consider a coupled system of m(>= 2) linear singularly perturbed equations of reaction-diffusion type coupled in the reaction terms with discontinuous source term. The leading term of each equation is multiplied by a small positive parameter. These singular perturbation parameters are assumed to be distinct in magnitude. Overlapping boundary and interior layers can appear in the solution. A numerical method is constructed that involve an appropriate piecewise-uniform Shishkin mesh, which is fitted to both the boundary and interior layers. The parameter-uniform convergence of the numerical approximations is examined.
We examine the use of Hermite interpolation, that is interpolation using derivative data, in place of Lagrange interpolation to develop high-order PDE solvers. The fundamental properties of Hermite interpolation are r...
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ISBN:
(纸本)9783319198002;9783319197999
We examine the use of Hermite interpolation, that is interpolation using derivative data, in place of Lagrange interpolation to develop high-order PDE solvers. The fundamental properties of Hermite interpolation are recalled, with an emphasis on their smoothing effect and robust performance for nonsmooth functions. Examples from the CHIDES library are presented to illustrate the construction and performance of Hermite methods for basic wave propagation problems.
We present a pipeline for the conversion of 3D models into a form suitable for isogeometric analysis (IGA). The input into our pipeline is a boundary represented 3D model, either as a triangulation or as a collection ...
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ISBN:
(数字)9783319233154
ISBN:
(纸本)9783319233154;9783319233147
We present a pipeline for the conversion of 3D models into a form suitable for isogeometric analysis (IGA). The input into our pipeline is a boundary represented 3D model, either as a triangulation or as a collection of trimmed non-uniform rational B-spline (NURBS) surfaces. The pipeline consists of three stages: computer aided design (CAD) model reconstruction from a triangulation (if necessary);segmentation of the boundary-represented solid into topological hexahedra;and volume parameterization. The result is a collection of volumetric NURBS patches. In this paper we discuss our methods for the three stages, and demonstrate the suitability of the result for IGA by performing stress simulations with examples of the output.
Isogeometric Analysis (IgA) uses the same class of basis functions for both representing the geometry of the computational domain and approximating the solution of the boundary value problem under consideration. In pr...
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ISBN:
(数字)9783319233154
ISBN:
(纸本)9783319233154;9783319233147
Isogeometric Analysis (IgA) uses the same class of basis functions for both representing the geometry of the computational domain and approximating the solution of the boundary value problem under consideration. In practical applications, geometrical patches are used in order to get flexibility in the geometrical representation. This multi-patch representation corresponds to a decomposition of the computational domain into non-overlapping subdomains also called patches in the geometrical framework. We will present discontinuous Galerkin (dG) methods that allow for discontinuities across the subdomain (patch) boundaries. The required interface conditions are weakly imposed by the dG terms associated with the boundary of the subdomains. The construction and the corresponding discretization error analysis of such dG multi-patch IgA schemes is given for heterogeneous diffusion model problems in volumetric 2d and 3d domains as well as on open and closed surfaces. The theoretical results are confirmed by numerous numerical experiments which have been performed in G+SMO. The concept and the main features of the IgA library G+SMO are also described.
It has been noted in the past that discontinuous Galerkin methods can be viewed as a low order multi-domain Spectral method with penalty term (Hesthaven et al., Spectral methods for time-dependent problems, Cambridge ...
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ISBN:
(纸本)9783319198002;9783319197999
It has been noted in the past that discontinuous Galerkin methods can be viewed as a low order multi-domain Spectral method with penalty term (Hesthaven et al., Spectral methods for time-dependent problems, Cambridge University Press, Cambridge, 2007). It is then logical to first ask how to relate filters in Spectral Methods to Smoothness-Increasing Accuracy-Conservin (SIAC) filters, which are typically applied to approximations obtained via the discontinuous Galerkin methods. In this article we make a first effort to relate Smoothness-Increasing Accuracy-Conserving filtering to filtering for Spectral Methods. We frame this discussion in the context of Vandeven (J Sci Comput 6: 159-192, 1991).
The work deals with numerical simulation of transonic turbulent flow in turbine cascades taking into account transition to turbulence. The Favre-averaged Navier-Stokes equations are closed by the SST eddy-viscosity tu...
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ISBN:
(纸本)9783319257273;9783319257259
The work deals with numerical simulation of transonic turbulent flow in turbine cascades taking into account transition to turbulence. The Favre-averaged Navier-Stokes equations are closed by the SST eddy-viscosity turbulence model or by explicit algebraic Reynolds stress turbulence model (EARSM) with the gamma-zeta transition model of Lodefier and Dick. The mathematical model is solved by implicit AUSM-type finite volume method. The implementation of transition model does not require case specific input under the assumption that the whole thickness of boundary layer is contained in the same block of multi-block grid, which can easily be fulfilled in the cases considered. The results are shown for 2D tip profile turbine cascade and 2D and 3D SE1050 turbine cascade.
We make an initial investigation into the temporal efficiency of a fully discrete summation-by-parts approach for stiff unsteady flows with boundary layers. As a model problem for the Navier-Stokes equations we consid...
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ISBN:
(纸本)9783319198002;9783319197999
We make an initial investigation into the temporal efficiency of a fully discrete summation-by-parts approach for stiff unsteady flows with boundary layers. As a model problem for the Navier-Stokes equations we consider a two-dimensional advection-diffusion problem with a boundary layer. The problem is discretized in space using finite difference approximations on summation-by-parts form together with weak boundary conditions, leading to optimal stability estimates. For the time integration part we consider various forms of high order summation-by-parts operators, and compare the results to an existing popular fourth order diagonally implicit Runge-Kutta method. To solve the resulting fully discrete equation system, we employ a multi-grid scheme with dual time stepping.
We propose and numerically investigate two approaches for extending the application area of transparent boundary conditions (TBCs) for the wave equation: a method for generating finite-difference approximations of TBC...
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ISBN:
(纸本)9783319198002;9783319197999
We propose and numerically investigate two approaches for extending the application area of transparent boundary conditions (TBCs) for the wave equation: a method for generating finite-difference approximations of TBCs with the fourth and sixth order in space, and a coupling procedure of TBCs on the top boundary of a cubical computational domain with characteristic BCs at the neighbor side boundaries.
In this paper, we consider the problem of reconstructing piecewise smooth functions to high accuracy from nonuniform samples of their Fourier transform. We use the framework of nonuniform generalized sampling (NUGS) t...
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ISBN:
(纸本)9783319198002;9783319197999
In this paper, we consider the problem of reconstructing piecewise smooth functions to high accuracy from nonuniform samples of their Fourier transform. We use the framework of nonuniform generalized sampling (NUGS) to do this, and to ensure high accuracy we employ reconstruction spaces consisting of splines or (piecewise) polynomials. We analyze the relation between the dimension of the reconstruction space and the bandwidth of the nonuniform samples, and show that it is linear for splines and piecewise polynomials of fixed degree, and quadratic for piecewise polynomials of varying degree.
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