共查询到20条相似文献,搜索用时 15 毫秒
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针对当前多介质流体计算中出现的速度和压强在介质界面处产生伪振荡的问题,我们设计了一种基于非平衡态的Lax-Friedrichs格式.我们构造的算法保证了多个守恒性质:总质量和分质量守恒,总动量和总能量守恒,它还可以保证分质量非负.更重要的是它消除了速度和压强在介质界面处的伪振荡.数值例子表明这一算法是有效的. 相似文献
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We consider the diagnostics of nonequilibrium gaseous media in a spatially one-dimensional formulation with the measurement
sensors placed in various flow cross-sections. The variational method minimizes the discrepancy functional over the system
of initial parameters allowing for the reliability, of the observations. A technique is developed for deriving the functional
gradient, which depends on the path components of the Cauchy problem calculated at various points. The gradient is shown to
be Lipschitz-continuous in control and the iterative gradient projection method converges to the set of stationary points
of the functional.
Translated from Prikladnaya Matematika i Informatika, Vol. 11, No. 1, pp. 78–85, 1999. 相似文献
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Various facets of the equilibrium statistical theories for large-scale coherent structures for two-dimensional flows with and without topography are studied here. The classical few-constraint statistical theories involving energy-enstrophy principles or point vortices are shown to be statistically sharp in the more recent statistical theories with an infinite number of constraints; in other words, at the macrostates of the few-constraint theories, the many-constraint theory provides no additional statistical information. These results are established through a general link between these statistical theories, generalized “selective decay” principles, and statistical sharpness. Through an asymptotic procedure, the many-constraint statistical theories for flows with topography and small-potential vorticity are shown to yield the simpler energy-enstrophy macroscopic states at leading order with systematic higher-order corrections involving a renormalized topography that includes higher moments of the microscopic potential vorticity distribution. For nonequilibrium flows with and without topography, the utility of crude approximate dynamics based on “adiabatic approximation” through the macrostates of few-constraint statistical theory is developed here. It is established that for nonequilibrium decaying flows with viscous dissipation, the crude dynamics based on macrostates involving statistical point vortices yields an excellent approximation; the role of “selective decay” principles is also clarified and compared quantitatively in this context through both mathematical theory and numerical experiments. Surprisingly, these approximate dynamics yield a much poorer approximation with moderate Ekman drag as the dissipative mechanism, and a simple analytical explanation is provided here. Finally, all of these issues are pursued more briefly for damped and driven flows with topography. © 1997 John Wiley & Sons, Inc. 相似文献
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Buoyancy driven flows of two Bingham fluids in an inclined ductare considered, providing a simplified model for many oilfieldcementing processes. The flows studied are near-uniaxial andstratified, with the heavy fluid moving down the incline, displacingthe lighter fluid upwards. Existence and uniqueness resultsare obtained for quite general flows and for those which satisfyan axial flow rate constraint. Parametric dependence of thesolutions on the axial pressure gradient is studied. Flows whichsatisfy a zero net axial flow constraint result from an axialpressure gradient which minimizes the viscous dissipation, butnot the plastic dissipation. A regularization method is usedto compute solutions to these problems for (more or less) arbitraryfluid-fluid interfaces and duct-cross sections. Examples relatedto a number of practical applications are presented. 相似文献
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《Chaos, solitons, and fractals》2000,11(8):1183-1190
We have considered the hierarchy of integrable systems associated with the unstable nonlinear Schrodinger equation. The spectral gradient approach and the trace identity are used to derive the bi-Hamiltonian structure of the system. The bi-Hamiltonian property and the square eigenfunctions determined via the spectral gradient approach are then used to construct constrained flows, which is also proved to be derivable from a rational Lax operator. This new Lax operator of the constrained flows is seen to generate the classical r-matrix. Lastly it is also explicitly demonstrated that the different integrals of motion of the constrained flows Poisson commute. 相似文献
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An index theory for flows is presented which extends the classical Morse theory for gradient flows on compact manifolds. The theory is used to prove a Morse-type existence statement for periodic solutions of a time-dependent (periodic in time) and asymptotically linear Hamiltonian equation. 相似文献
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P. K. Galenko V. G. Lebedev A. A. Sysoeva 《Computational Mathematics and Mathematical Physics》2011,51(6):1074-1090
The critical dynamics of a spatially inhomogeneous system are analyzed with allowance for local nonequilibrium, which leads
to a singular perturbation in the equations due to the appearance of a second time derivative. An extension is derived for
the Eyre theorem, which holds for classical critical dynamics described by first-order equations in time and based on the
local equilibrium hypothesis. It is shown that gradient-stable numerical algorithms can also be constructed for second-order
equations in time by applying the decomposition of the free energy into expansive and contractive parts, which was suggested
by Eyre for classical equations. These gradient-stable algorithms yield a monotonically nondecreasing free energy in simulations
with an arbitrary time step. It is shown that the gradient stability conditions for the modified and classical equations of
critical dynamics coincide in the case of a certain time approximation of the inertial dynamics relations introduced for describing
local nonequilibrium. Model problems illustrating the extended Eyre theorem for critical dynamics problems are considered. 相似文献
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Isaac Vikram Chenchiah Marc Oliver Rieger Johannes Zimmer 《Nonlinear Analysis: Theory, Methods & Applications》2009,71(11):5820-5834
This article is concerned with gradient flows in asymmetric metric spaces, that is, spaces with a topology induced by an asymmetric metric. Such an asymmetry appears naturally in many applications, e.g., in mathematical models for materials with hysteresis. A framework of asymmetric gradient flows is established under the assumption that the metric is weakly lower-semicontinuous in the second argument (and not necessarily on the first), and an existence theorem for gradient flows defined on an asymmetric metric space is given. 相似文献
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We consider the dynamics of vector fields on three-manifolds which are constrained to lie within a plane field, such as occurs
in nonholonomic dynamics. On compact manifolds, such vector fields force dynamics beyond that of a gradient flow, except in
cases where the underlying manifold is topologically simple (i.e., a graph-manifold). Furthermore, there are strong restrictions on the types of gradient flows realized within plane fields:
such flows lie on the boundary of the space of nonsingular Morse-Smale flows. This relationship translates to knot-theoretic
obstructions for the link of singularities in the flow. In the case of an integrable plane field, the restrictions are even
finer, forcing taut foliations on surface bundles. The situation is completely different in the case of contact plane fields,
however: it is easy to realize gradient fields within overtwisted contact structures (the nonintegrable analogue of a foliation
with Reeb components).
Received: December 9, 1997. 相似文献
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《Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire》2020,37(2):239-279
Inspired by recent work on minimizers and gradient flows of constrained interaction energies, we prove that these energies arise as the slow diffusion limit of well-known aggregation-diffusion energies. We show that minimizers of aggregation-diffusion energies converge to a minimizer of the constrained interaction energy and gradient flows converge to a gradient flow. Our results apply to a range of interaction potentials, including singular attractive and repulsive-attractive power-law potentials. In the process of obtaining the slow diffusion limit, we also extend the well-posedness theory for aggregation-diffusion equations and Wasserstein gradient flows to admit a wide range of nonconvex interaction potentials. We conclude by applying our results to develop a numerical method for constrained interaction energies, which we use to investigate open questions on set valued minimizers. 相似文献
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T. V. Bashutskaya A. E. Grishchenko V. N. Sklepovoi 《Journal of Mathematical Sciences》1992,58(5):461-465
An approach is proposed to computer simulation of gas-dynamic processes in chemically nonequilibrium flows in supersonic nozzles. An algorithm for the solution of the problem is developed. Convergence of iterative processes and stability of the linearized problem are investigated.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 58, pp. 89–95, 1986. 相似文献
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Jiajie Li & Shengfeng Zhu 《计算数学(英文版)》2022,40(2):231-257
We consider optimal shape design in Stokes flow using $H^1$ shape gradient flows based on the distributed Eulerian derivatives. MINI element is used for discretizations of Stokes equation and Galerkin finite element is used for discretizations of distributed and boundary $H^1$ shape gradient flows. Convergence analysis with a priori error estimates is provided under general and different regularity assumptions. We investigate the performances of shape gradient descent algorithms for energy dissipation minimization and obstacle flow. Numerical comparisons in 2D and 3D show that the distributed $H^1$ shape gradient flow is more accurate than the popular boundary type. The corresponding distributed shape gradient algorithm is more effective. 相似文献
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A. L. Ankudinov 《Computational Mathematics and Mathematical Physics》2010,50(8):1427-1432
The two-dimensional nonequilibrium hypersonic free jet boundary layer gas flow in the near wake of a body is studied using
a closed system of macroscopic equations obtained (as a thin-layer version) from moment equations of kinetic origin for a
polyatomic single-component gas with internal degrees of freedom. (This model is can be used to study flows with strong violations
of equilibrium with respect to translational and internal degrees of freedom.) The solution of the problem under study (i.e.,
the kinetic model of a nonequilibrium homogeneous polyatomic gas flow in a free jet boundary layer) is shown to be related
to the known solution of the well-studied simpler problem of a Navier-Stokes free jet boundary layer, and a method based on
this relation is proposed for solving the former problem. It is established that the gas flow velocity distribution along
the separating streamline in the kinetic problem of a free jet boundary layer coincides with the distribution obtained by
solving the Navier-Stokes version of the problem. It is found that allowance for the nonequilibrium nature of the flow with
respect to the internal and translational degrees of freedom of a single-component polyatomic gas in a hypersonic free jet
boundary layer has no effect on the base pressure and the wake angle. 相似文献
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Pursued herein are the closed-form solutions of the Navier–Stokes equations for both planar channel and circular duct flows, influenced by either periodic or aperiodic pressure gradients, of which the amplitudes are sufficiently low to yield laminar incompressible flows. The analyses conducted for the unsteady flows parallel to the walls lead to the analytical solutions that encompass not only the long-time oscillations by periodic pressure gradients, but also the transient start-up flows commencing from zero velocity due to arbitrary aperiodic pressure gradients. With the standard methods employed, the present solutions generalizing the classic ones are written in the forms rendering the explicit dependence on the pressure gradient, and are numerically validated by the existing solutions of simple sinusoidal oscillations and a flow involving an aperiodic impulsive pressure gradient. By virtue of their functional forms, the present solutions can be applied with any pressure gradients, even if the gradients are not in closed forms. 相似文献
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A model kinetic equation approximating the Boltzmann equation in a wide range of nonequilibrium gas states was constructed
to describe rarefied gas flows. The kinetic model was based on a distribution function depending on the absolute velocity
of the gas particles. Highly efficient in numerical computations, the model kinetic equation was used to compute a shock wave
structure. The numerical results were compared with experimental data for argon. 相似文献
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We solve the problem of a nonequilibrium adiabatically expanding flow of a reacting gas in a short supersonic nozzle allowing for the effect of flow expansion and the gradients of gas-dynamic parameters on the electron-chemical kinetics of the processes in the reagent mixture. The possibility of obtaining population inversion of the electronic terms of molecules in such flows is investigated. The emission capacity of bromine and chlorine is studied.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 55, pp. 101–106, 1985. 相似文献
19.
On Finite Element Approximations to a Shape Gradient Flow in Shape Optimization of Elliptic Problems
Chunxiao Liu & Shengfeng Zhu 《计算数学(英文版)》2023,41(5):957-980
Shape gradient flows are widely used in numerical shape optimization algorithms. We investigate the accuracy and effectiveness of approximate shape gradients flows for shape optimization of elliptic problems. We present convergence analysis with a priori error estimates for finite element approximations of shape gradient flows associated with a distributed or boundary expression of Eulerian derivative. Numerical examples are presented to verify theory and show that using the volume expression is effective for shape optimization with Dirichlet and Neumann boundary conditions. 相似文献
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W. S. Wong 《Journal of Optimization Theory and Applications》1995,87(1):197-220
Over the past decade, a number of connections between continuous flows and numerical algorithms were established. Recently, Brockett and Wong reported a connection between gradient flows on the special orthogonal groupLO(n) and local search solutions for the assignment problem. In this paper, we describe a uniform formulation for certain NP-hard combinatorial optimization problems in matrix form and examine their connection with gradient flows onLO(n). For these problems, there is a correspondence between the so-called 2-opt solutions and asymptotically stable critical points of an associated gradient flow. 相似文献