We present a mathematical and numerical model for non-isothermal, compressible flow of a mixture of two ideal gases subject to gravity. This flow is described by the balance equations for mass, momentum and energy tha...
详细信息
ISBN:
(纸本)9783319399294;9783319399270
We present a mathematical and numerical model for non-isothermal, compressible flow of a mixture of two ideal gases subject to gravity. This flow is described by the balance equations for mass, momentum and energy that are solved numerically by the scheme based on themethod of lines. The spatial discretization is carried out by means of the finite volume method, where the staggered arrangement of variables is employed. The time integration is realized by the Runge-KuttaMerson method. The article also contains test results obtained by the presented
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...
详细信息
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.
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...
详细信息
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...
详细信息
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.
Two efficient spectral-element methods, based on Legendre and Laguerre polynomials respectively, are derived for direct approximation of the electronic Schrodinger equation in one spatial dimension. Compared to existi...
详细信息
ISBN:
(数字)9783319282626
ISBN:
(纸本)9783319282626;9783319282602
Two efficient spectral-element methods, based on Legendre and Laguerre polynomials respectively, are derived for direct approximation of the electronic Schrodinger equation in one spatial dimension. Compared to existing literatures, a spectral-element approach is used to treat the singularity in nucleus-electron Coulomb potential, and with the help of Slater determinant, special basis functions are constructed to obey the antisymmetric property of the fermionic wavefunctions. Numerical tests are presented to show the efficiency and accuracy of the proposed methods.
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 ...
详细信息
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.
暂无评论