The space time CE/SE method for solving one-dimensional batch crystallization model with fines dissolution

This article is concerned with the numerical investigation of one-dimensional population balance models for batch crystallization process with fines dissolution.In batch crystallization,dissolution of smaller unwanted nuclei below some critical size is of vital importance as it improves the quality of product.The crystal growth rates for both size-independent and size-dependent cases are considered.A delay in recycle pipe is also included in the model.The space–time conservation element and solution element method,originally derived for non-reacting flows,is used to solve the model.This scheme has already been applied to a range of PDEs,mainly in the area of fluid mechanics.The numerical results are compared with those obtained from the Koren scheme,showing that the proposed scheme is more efficient.

Multi-symplectic method for generalized Boussinesq equation

The generalized Boussinesq equation that represents a group of important nonlinear equations possesses many interesting properties. Multi-symplectic formulations of the generalized Boussinesq equation in the Hamilton space are introduced in this paper. And then an implicit multi-symplectic scheme equivalent to the multi-symplectic Box scheme is constructed to solve the partial differential equations （PDEs） derived from the generalized Boussinesq equation. Finally, the numerical experiments on the soliton solutions of the generalized Boussinesq equation are reported. The results show that the multi-symplectic method is an efficient algorithm with excellent long-time numerical behaviors for nonlinear partial differential equations.

A three-dimensional Eulerian method for the numerical simulation of high-velocity impact problems

In the present paper, a three-dimensional （3D） Eulerian technique for the 3D numerical simulation of high-velocity impact problems is proposed. In the Eulerian framework, a complete 3D conservation element and solution element scheme for conservative hyperbolic governing equations with source terms is given. A modified ghost fluid method is proposed for the treatment of the boundary conditions. Numerical simulations of the Taylor bar problem and the ricochet phenomenon of a sphere impacting a plate target at an angle of 60~ are carried out. The numerical results are in good agreement with the corresponding experimental observations. It is proved that our computational technique is feasible for analyzing 3D high-velocity impact problems.

THE APPLICATION OF THE ASYMPTOTIC METHOD TO A CLASS OF STRONGLY NONLINEAR SYSTEMS

In this paper, according to the form of the asymptotic solution of papers [1, 2], the asymptotic method is extended to the following a class of more general strong nonlinear vibration systemswhere g and f are the nonlinear analytical-functions of x and x, and e>0 is a small parameter. We assume that the derivative system corresponding to e=0 has periodic solution. The recurrence equations of the asymptotic solution for the system (0.1) are deduced in this paper, and they are applied to practical examples.

THE GENERIC PROPERTIES OF SOLUTIONS OF A CONSERVATION LAW

In this paper we answer all the questions about the conjectures of Glimm and Lax on genericproperties of solutions. We prove that the discotinuous points of almost every solution with L∞,bounded varistion or contrinuous data are dense in the upper half-plane minus the closure of the setof central simple waves. It is also proved that if the equation is analytic,then the solutions withpiecewise analytic data are piecewise analytic,and the shock curves are also piecewise analytic. Wedisprove the conjecture which claims that almost every solution with C^k data is 'bad' enough, and provethat every solution with C^k data possesses nice propetied, i.e. when k≥4 the generic property ofsolutions is piecewise C^k,and hence is 'good' enough.For the proof of the generic property withC^k (k≥4) data, the idea of transversality in the theory of singular points is essential.

Modeling the Earth's magnetosphere under the influence of solar wind with due northward IMF by the AMR-CESE-MHD model

We present a newly developed global magnetohydrodynamic(MHD) model to study the responses of the Earth's magnetosphere to the solar wind. The model is established by using the space-time conservation element and solution element(CESE) method in general curvilinear coordinates on a six-component grid system. As a preliminary study, this paper is to present the model's numerical results of the quasi-steady state and the dynamics of the Earth's magnetosphere under steady solar wind flow with due northward interplanetary magnetic field(IMF). The model results are found to be in good agreement with those published by other numerical magnetospheric models.

Comparison of the performance of traditional advection-dispersion equation and mobile-immobile model for simulating solute transport in heterogeneous soils

The traditional advection-dispersion equation(ADE) and the mobile-immobile model(MIM) are widely used to describe solute transport in heterogeneous porous media. However, the fitness of the two models is casedependent. In this paper, the transport of conservative,adsorbing and degradable solutes through a 1 m heterogeneous soil column under steady flow condition was simulated by ADE and MIM, and sensitivity analysis was conducted. Results show that MIM tends to prolong the breakthrough process and decrease peak concentration for all three solutes, and tailing and skewness are more pronounced with increasing dispersivity. Breakthrough curves of the adsorbing solute simulated by MIM are less sensitive to the retardation factor compared with the results simulated by ADE. The breakthrough curves of degradable solute obtained by MIM and ADE nearly overlap with a high degradation rate coefficient, indicating that MIM and ADE perform similarly for simulating degradable solute transport when biochemical degradation prevails over the mass exchange between mobile and immobile zones. The results suggest that the physical significance of dispersivity should be carefully considered when MIM is applied to simulate the degradable solute transport and/or ADE is applied to simulate the adsorbing solute transport in highly dispersive soils.