We present the dual reciprocity boundary element method (DRBEM) solution of the system of equations which model magnetohydrodynamic (MHD) flow in a pipe with moving lid at low magnetic Reynolds number. The external ma...
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ISBN:
(纸本)9783319399294;9783319399270
We present the dual reciprocity boundary element method (DRBEM) solution of the system of equations which model magnetohydrodynamic (MHD) flow in a pipe with moving lid at low magnetic Reynolds number. The external magnetic field acts in the pipe-axis direction generating the electric potential. The solution is obtained in terms of stream function, vorticity and electric potential in the cross-section of the pipe, and the pipe axis velocity is also computed under a constant pressure gradient. It is found that fluid flow concentrates through the upper right corner forming boundary layers with the effect of moving lid and increased magnetic field intensity. Electric field behavior is changed accordingly with the insulated and conducting portions of the pipe walls. Fluid moves in the pipe-axis direction with an increasing rate of magnitude when Hartmann number increases. The boundary only nature of DRBEM provides the solution at a low computational expense.
We consider Galerkin approximation in space of linear parabolic initialboundary value problems where the elliptic operator is symmetric and thus induces an energy norm. For two related variational settings, we show th...
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ISBN:
(纸本)9783319399294;9783319399270
We consider Galerkin approximation in space of linear parabolic initialboundary value problems where the elliptic operator is symmetric and thus induces an energy norm. For two related variational settings, we show that the quasioptimality constant equals the stability constant of the L-2- projection with respect to that energy norm.
In this paper we review various numerical homogenization methods for monotone parabolic problems with multiple scales. The spatial discretisation is based on finite element methods and the multiscale strategy relies o...
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ISBN:
(纸本)9783319416403;9783319416380
In this paper we review various numerical homogenization methods for monotone parabolic problems with multiple scales. The spatial discretisation is based on finite element methods and the multiscale strategy relies on the heterogeneous multiscale method. The time discretization is performed by several classes of Runge-Kutta methods (strongly A-stable or explicit stabilized methods). We discuss the construction and the analysis of such methods for a range of problems, from linear parabolic problems to nonlinear monotone parabolic problems in the very general L-p(W-1,W-p) setting. We also show that under appropriate assumptions, a computationally attractive linearized method can be constructed for nonlinear problems.
A comparison study of different decoupled schemes for the evolutionary Stokes/Darcy problem is carried out. Stability and error estimates of a mass conservative multiple-time-step algorithm are provided under a time s...
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In this paper, we show a local a priori error estimate for the Poisson equation in three space dimensions (3D), where the source term is a Dirac measure concentrated on a line. This type of problem can be found in man...
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ISBN:
(纸本)9783319399294;9783319399270
In this paper, we show a local a priori error estimate for the Poisson equation in three space dimensions (3D), where the source term is a Dirac measure concentrated on a line. This type of problem can be found in many application areas. In medical engineering, e.g., blood flow in capillaries and tissue can be modeled by coupling Poiseuille's and Darcy's law using a line source term. Due to the singularity induced by the line source term, finite element solutions converge suboptimal in classical norms. However, quite often the error at the singularity is either dominated by model errors (e.g. in dimension reduced settings) or is not the quantity of interest (e.g. in optimal control problems). Therefore we are interested in local error estimates, i.e., we consider in space a L-2-norm on a fixed subdomain excluding a neighborhood of the line, where the Dirac measure is concentrated. It is shown that linear finite elements converge optimal up to a log-factor in such a norm. The theoretical considerations are confirmed by some numerical tests.
In this study, possibility of reducing drag in turbulent pipe flow via phase randomization is investigated. Phase randomization is a passive drag reduction mechanism, the main idea behind which is, reduction in drag c...
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ISBN:
(纸本)9783319399294;9783319399270
In this study, possibility of reducing drag in turbulent pipe flow via phase randomization is investigated. Phase randomization is a passive drag reduction mechanism, the main idea behind which is, reduction in drag can be obtained via distrupting the wave-like structures present in the flow. To facilitate the investigation flow in a circular cylindrical pipe is simulated numerically. DNS (direct numerical simulation) approach is used with a solenoidal spectral formulation, hence the continuity equation is automatically satisfied (Tugluk and Tarman, Acta Mech 223(5): 921-935, 2012). Simulations are performed for flow driven by a constant mass flux, at a bulk Reynolds number (Re) of 4900. Legendre polynomials are used in constructing the solenoidal basis functions employed in the numerical method.
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