The purpose of this paper is to extend a novel numerical methodology, combining thermal immersed boundary and Fourier pseudospectral methods called IMERSPEC. This methodology has been developed for incompressible flui...
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ISBN:
(纸本)9783319198002;9783319197999
The purpose of this paper is to extend a novel numerical methodology, combining thermal immersed boundary and Fourier pseudospectral methods called IMERSPEC. This methodology has been developed for incompressible fluid flow problems modeled using Navier-Stokes, mass and energy equations. The numerical algorithm consists of Fourier pseudospectral method (FPSM), where Dirichlet boundary condition is modeled using an immersed boundary method (multi-direct forcing method). The new method combines the advantages of high accuracy and low computational cost provided by FPSM to the possibility of managing complex and non periodical geometries given by immersed boundary method. In the present work this new methodology is applied to the problem of heat transfer for natural convection in the annulus between horizontal concentric cylinders and conducted to validate the capability and efficiency of present method. Results for this application are presented and good agreement with available data in the literature have been achieved.
We examine a time dependent singularly perturbed convection-diffusion problem, where the convective coefficient contains an interior layer. A smooth transformation is introduced to align the grid to the location of th...
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ISBN:
(纸本)9783319257273;9783319257259
We examine a time dependent singularly perturbed convection-diffusion problem, where the convective coefficient contains an interior layer. A smooth transformation is introduced to align the grid to the location of the interior layer. A numerical method consisting of an upwinded finite difference operator and a piecewise-uniform Shishkin mesh is constructed in this transformed domain. Numerical results are presented which indicate that the numerical approximations converge at a rate of first order (up to logarithmic factors) uniformly in the pointwise maximum norm.
Filtering is necessary to stabilize piecewise smooth solutions. The resulting diffusion stabilizes the method, but may fail to resolve the solution near discontinuities. Moreover, high order filtering still requires c...
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ISBN:
(纸本)9783319198002;9783319197999
Filtering is necessary to stabilize piecewise smooth solutions. The resulting diffusion stabilizes the method, but may fail to resolve the solution near discontinuities. Moreover, high order filtering still requires cost prohibitive time stepping. This paper introduces an adaptive filter that controls spurious modes of the solution, but is not unnecessarily diffusive. Consequently we are able to stabilize the solution with larger time steps, but also take advantage of the accuracy of a high order filter.
High-order finite-differencemethods are commonly used in wave propagator for industrial subsurface imaging algorithms. computational aspects of the reduced linear elastic vertical transversely isotropic propagator are...
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ISBN:
(纸本)9783319198002;9783319197999
High-order finite-differencemethods are commonly used in wave propagator for industrial subsurface imaging algorithms. computational aspects of the reduced linear elastic vertical transversely isotropic propagator are considered. Thread parallel algorithms suitable for implementing this propagator on multi-core and many-core processing devices are introduced. Portability is addressed through the use of the OCCA runtime programming interface. Finally, performance results are shown for various architectures on a representative synthetic test case.
A windowed Fourier method is proposed for approximation of non-periodic functions on equispaced nodes. Spectral convergence is obtained in most of the domain, except near the boundaries, where polynomial least-squares...
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ISBN:
(纸本)9783319198002;9783319197999
A windowed Fourier method is proposed for approximation of non-periodic functions on equispaced nodes. Spectral convergence is obtained in most of the domain, except near the boundaries, where polynomial least-squares is used to correct the approximation. Because the method can be implemented using partition of unit and domain decomposition, it is suitable for adaptive and parallel implementations and large scale computations. Computations can be carried out using fast Fourier transforms. Comparisons with Fourier extension, rational interpolation and least-squares methods are presented.
In this paper the numerical approximation of turbulent and laminar incompressible turbulent flow is considered. The mathematical model is either based on incompressible Navier-Stokes equations or on Reynolds averaged ...
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ISBN:
(纸本)9783319257273;9783319257259
In this paper the numerical approximation of turbulent and laminar incompressible turbulent flow is considered. The mathematical model is either based on incompressible Navier-Stokes equations or on Reynolds averaged Navier-Stokes (RANS) equations enclosed by a turbulence model. The problem is discretized in space by the finite element method, the detailed description of the stabilization shall be given and several aspects of approximation of the turbulence/transition model shall be given. The numerical results of the finite elementmethod shall be presented.
A two-point boundary value problem whose highest-order term is a Riemann-Liouville fractional derivative of order delta epsilon (1, 2)is considered on the interval [0,1]. It is shown that the solution u of the problem...
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ISBN:
(纸本)9783319257273;9783319257259
A two-point boundary value problem whose highest-order term is a Riemann-Liouville fractional derivative of order delta epsilon (1, 2)is considered on the interval [0,1]. It is shown that the solution u of the problem lies in C[0, 1] but not in C-1[0,1] because u'(x) blows up at x -> 0 for each fixed value of delta. Furthermore, u'(1) blows up as delta -> 1(+) if and only if the constant convection coefficient b satisfies b >= 1.
This paper presents a curved meshing technique for unstructured tetrahedral meshes where G(1) surface continuity is maintained for the triangular element faces representing the curved domain surfaces. A bottom-up curv...
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ISBN:
(纸本)9783319198002;9783319197999
This paper presents a curved meshing technique for unstructured tetrahedral meshes where G(1) surface continuity is maintained for the triangular element faces representing the curved domain surfaces. A bottom-up curving approach is used to support geometric models with multiple surface patches where either C-0 or G(1) geometry continuity between patches is desired. Specific parametrization approaches based on Bezier forms and blending functions are used to define the mapping for curved element faces and volumes between parametric and physical coordinate systems. A preliminary result demonstrates that using G(1)-continuity meshes can improve the solution results obtained.
Experiences from using a higher order accurate finite difference multi-block solver to compute the time dependent flow over a cavity is summarized. The work has been carried out as part of a work in a European project...
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ISBN:
(纸本)9783319198002;9783319197999
Experiences from using a higher order accurate finite difference multi-block solver to compute the time dependent flow over a cavity is summarized. The work has been carried out as part of a work in a European project called IDIHOM in a collaboration between the Swedish Defense Research Agency (FOI) and University of Linkping (LiU). The higher order code is based on Summation By Parts operators combined with the Simultaneous Approximation Term approach for boundary and interface conditions. The spatial accuracy of the code is verified by calculations over a cyclinder by monitoring the decay of the errors of known wall quantities as the grid is refined. The focus is on the validation for a test case of transonic flow over a rectangular cavity with hybrid RANS/LES calculations. The results are compared to reference numerical results from a second order finite volume code as well as with experimental results with a good overall agreement between the results.
Designing numerical methods with high-order accuracy for problems in irregular domains and/or with interfaces is crucial for the accurate solution of many problems with physical and biological applications. The major ...
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ISBN:
(纸本)9783319198002;9783319197999
Designing numerical methods with high-order accuracy for problems in irregular domains and/or with interfaces is crucial for the accurate solution of many problems with physical and biological applications. The major challenge here is to design an efficient and accurate numerical method that can capture certain properties of analytical solutions in different domains/subdomains while handling arbitrary geometries and complex structures of the domains. Moreover, in general, any standard method (finite-difference, finite-element, etc.) will fail to produce accurate solutions to interface problems due to discontinuities in the model's parameters/solutions. In this work, we consider Difference Potentials Method (DPM) as an efficient and accurate solver for the variable coefficient elliptic interface problems.
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