Parallel overlapping Schwarz preconditioners are considered and applied to the structural block in monolithic fluid-structure interaction (FSI). The twolevel overlapping Schwarz method uses a coarse level based on ene...
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ISBN:
(纸本)9783319399294;9783319399270
Parallel overlapping Schwarz preconditioners are considered and applied to the structural block in monolithic fluid-structure interaction (FSI). The twolevel overlapping Schwarz method uses a coarse level based on energy minimizing functions. Linear elastic as well as nonlinear, anisotropic hyperelastic structural models are considered in an FSI problem of a pressure wave in a tube. Using our recent parallel implementation of a two-level overlapping Schwarz preconditioner based on the Trilinos library, the total computation time of our FSI benchmark problem was reduced by more than a factor of two compared to the algebraic onelevel overlapping Schwarz method used previously. Finally, also strong scalability for our FSI problem is shown for up to 512 processor cores.
In this paper we investigate the stability of the space-time discontinuous Galerkin method (STDGM) for the solution of nonstationary, linear convectiondiffusion- reaction problem in time-dependent domains formulated w...
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ISBN:
(纸本)9783319399294;9783319399270
In this paper we investigate the stability of the space-time discontinuous Galerkin method (STDGM) for the solution of nonstationary, linear convectiondiffusion- reaction problem in time-dependent domains formulated with the aid of the arbitrary Lagrangian-Eulerian (ALE) method. At first we define the continuous problem and reformulate it using the ALE method, which replaces the classical partial time derivative with the so called ALE-derivative and an additional convective term. In the second part of the paper we discretize our problem using the space-time discontinuous Galerkin method. The space discretization uses piecewise polynomial approximations of degree p >= 1, in time we use only piecewise linear discretization. Finally in the third part of the paper we present our results concerning the unconditional stability of the method.
We review basic design principles underpinning the construction of the mimetic finite difference and a few finite volume and finite element schemes for mixed formulations of elliptic problems. For a class of low-order...
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ISBN:
(纸本)9783319416403;9783319416380
We review basic design principles underpinning the construction of the mimetic finite difference and a few finite volume and finite element schemes for mixed formulations of elliptic problems. For a class of low-order mixed-hybrid schemes, we show connections between these principles and prove that the consistency and stability conditions must lead to a member of the mimetic family of schemes regardless of the selected discretization framework. Finally, we give two examples of using flexibility of the mimetic framework: derivation of arbitrary-order schemes and inexpensive convergent schemes for nonlinear problems with small diffusion coefficients.
We present an extension of the complete flux scheme for conservation laws containing a linear source. In our new scheme, we split off the linear part of the source and incorporate this term in the homogeneous flux, th...
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ISBN:
(纸本)9783319399294;9783319399270
We present an extension of the complete flux scheme for conservation laws containing a linear source. In our new scheme, we split off the linear part of the source and incorporate this term in the homogeneous flux, the remaining nonlinear part is included in the inhomogeneous flux. This approach gives rise to modified homogeneous and inhomogeneous fluxes, which reduce to the classical fluxes for vanishing linear source. On the other hand, if the linear source is large, the solution of the underlying boundary value problem is oscillatory, resulting in completely different numerical fluxes. We demonstrate the performance of the homogeneous flux approximation.
The two-dimensional, laminar, unsteady natural convection flow of a micropolar nanofluid (Al2O3-water) in a square enclosure under the influence of a magnetic field, is solved numerically using the Chebyshev spectral ...
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ISBN:
(纸本)9783319399294;9783319399270
The two-dimensional, laminar, unsteady natural convection flow of a micropolar nanofluid (Al2O3-water) in a square enclosure under the influence of a magnetic field, is solved numerically using the Chebyshev spectral collocation method (CSCM). The nanofluid is considered as Newtonian and incompressible, and the nanoparticles and water are assumed to be in thermal equilibrium. The governing equations in nondimensional form are given in terms of stream function, vorticity, micrototaion and temperature. The coupled and nonlinear equations are solved iteratively in the time direction, and an implicit backward difference scheme is employed for the time integration. The boundary conditions of vorticity are computed within this iterative process using a CSCM discretization of the stream function equation. The main advantages of CSCM, such as the high accuracy and the ease of implementation, aremade used of to obtain solutions for very high values of Ra and Ha, up to 10(7) and 1000, respectively.
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