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# Fictitious boundary and moving mesh methods for the numerical simulation of particulate flow

Institute of Applied Mathematics (LS III), University of Dortmund, 44227, Dortmund, Germany; Institute of Applied Mathematics (LS III), University of Dortmund, 44227, Dortmund, Germany; School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, 200030, China

01/2006; - Citations (19)
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**ABSTRACT:**We develop and analyze a numerical method for creating an adaptive moving grid in one-, two-, and three-dimensional regions. The method distributes grid nodes according to a given analytic or discrete weight function of the spatial and time variables, which reflects the fine structure of the solution. The weight function defines a vector field, which is used to construct a transformation of the computational domain into the physical domain. We prove that the resulting grid has the prescribed cell sizes and that no “mesh tangling” occurs. Numerical implementation of the method utilizes an efficient and robust least-squares solver to compute the vector field and a fourth-order Runge-Kutta scheme to determine the transformation. Results of several numerical experiments in one- and two-dimensions are also presented. These results indicate, among other things, that the method accurately redistributes the nodes and does not tangle the mesh. © 1996 John Wiley & Sons, Inc.Numerical Methods for Partial Differential Equations 01/1996; 12(4):489-506. · 1.21 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**Since the initial publication of Hu et al. (1992, Theor. Comput. Fluid Dyn.3, 285), the numerical method developed for direct simulations of fluid–solid systems using the arbitrary Lagrangian–Eulerian (ALE) technique has undergone continuous modifications. Some of the modifications were described in H. H. Hu (1996, Int. J. Multiphase Flow22, 335). In this paper, we will present the most up-to-date implementation of the method and the results of several benchmark test problems.Journal of Computational Physics 01/2001; · 2.14 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**A Lagrange-multiplier-based fictitious-domain method (DLM) for the direct numerical simulation of rigid particulate flows in a Newtonian fluid was presented previously. An important feature of this finite element based method is that the flow in the particle domain is constrained to be a rigid body motion by using a well-chosen field of Lagrange multipliers. The constraint of rigid body motion is represented by u=U+ω×r; u being the velocity of the fluid at a point in the particle domain; U and ω are the translational and angular velocities of the particle, respectively; and r is the position vector of the point with respect to the center of mass of the particle. The fluid–particle motion is treated implicitly using a combined weak formulation in which the mutual forces cancel. This formulation together with the above equation of constraint gives an algorithm that requires extra conditions on the space of the distributed Lagrange multipliers when the density of the fluid and the particles match. In view of the above issue a new formulation of the DLM for particulate flow is presented in this paper. In this approach the deformation rate tensor within the particle domain is constrained to be zero at points in the fluid occupied by rigid solids. This formulation shows that the state of stress inside a rigid body depends on the velocity field similar to pressure in an incompressible fluid. The new formulation is implemented by modifying the DLM code for two-dimensional particulate flows developed by others. The code is verified by comparing results with other simulations and experiments.International Journal of Multiphase Flow 09/2000; · 1.72 Impact Factor

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