60,306 research outputs found
Sweeping Preconditioner for the Helmholtz Equation: Moving Perfectly Matched Layers
This paper introduces a new sweeping preconditioner for the iterative
solution of the variable coefficient Helmholtz equation in two and three
dimensions. The algorithms follow the general structure of constructing an
approximate factorization by eliminating the unknowns layer by layer
starting from an absorbing layer or boundary condition. The central idea of
this paper is to approximate the Schur complement matrices of the factorization
using moving perfectly matched layers (PMLs) introduced in the interior of the
domain. Applying each Schur complement matrix is equivalent to solving a
quasi-1D problem with a banded LU factorization in the 2D case and to solving a
quasi-2D problem with a multifrontal method in the 3D case. The resulting
preconditioner has linear application cost and the preconditioned iterative
solver converges in a number of iterations that is essentially indefinite of
the number of unknowns or the frequency. Numerical results are presented in
both two and three dimensions to demonstrate the efficiency of this new
preconditioner.Comment: 25 page
A Robust Solution Procedure for Hyperelastic Solids with Large Boundary Deformation
Compressible Mooney-Rivlin theory has been used to model hyperelastic solids,
such as rubber and porous polymers, and more recently for the modeling of soft
tissues for biomedical tissues, undergoing large elastic deformations. We
propose a solution procedure for Lagrangian finite element discretization of a
static nonlinear compressible Mooney-Rivlin hyperelastic solid. We consider the
case in which the boundary condition is a large prescribed deformation, so that
mesh tangling becomes an obstacle for straightforward algorithms. Our solution
procedure involves a largely geometric procedure to untangle the mesh: solution
of a sequence of linear systems to obtain initial guesses for interior nodal
positions for which no element is inverted. After the mesh is untangled, we
take Newton iterations to converge to a mechanical equilibrium. The Newton
iterations are safeguarded by a line search similar to one used in
optimization. Our computational results indicate that the algorithm is up to 70
times faster than a straightforward Newton continuation procedure and is also
more robust (i.e., able to tolerate much larger deformations). For a few
extremely large deformations, the deformed mesh could only be computed through
the use of an expensive Newton continuation method while using a tight
convergence tolerance and taking very small steps.Comment: Revision of earlier version of paper. Submitted for publication in
Engineering with Computers on 9 September 2010. Accepted for publication on
20 May 2011. Published online 11 June 2011. The final publication is
available at http://www.springerlink.co
Using the generalized interpolation material point method for fluid-solid interactions induced by surface tension
This thesis is devoted to the development of new, Generalized Interpolation Material Point Method (GIMP)-based algorithms for handling surface tension and contact (wetting) in fluid-solid interaction (FSI) problems at small scales. In these problems, surface tension becomes so dominant that its influence on both fluids and solids must be considered. Since analytical solutions for most engineering problems are usually unavailable, numerical methods are needed to describe and predict complicated time-dependent states in the solid and fluid involved due to surface tension effects. Traditional computational methods for handling fluid-solid interactions may not be effective due to their weakness in solving large-deformation problems and the complicated coupling of two different types of computational frameworks: one for solid, and the other for fluid. On the contrary, GIMP, a mesh-free algorithm for solid mechanics problems, is numerically effective in handling problems involving large deformations and fracture. Here we extend the capability of GIMP to handle fluid dynamics problems with surface tension, and to develop a new contact algorithm to deal with the wetting boundary conditions that include the modeling of contact angle and slip near the triple points where the three phases -- fluid, solid, and vapor -- meet. The error of the new GIMP algorithm for FSI problems at small scales, as verified by various benchmark problems, generally falls within the 5% range. In this thesis, we have successfully extended the capability of GIMP for handling FSI problems under surface tension in a one-solver numerical framework, a unique and innovative approach.Chapter 1. Introduction -- Chapter 2. Using the generalized interpolation material point method for fluid dynamics at low reynolds numbers -- Chapter 3. On the modeling of surface tension and its applications by the generalized interpolation material point method -- Chapter 4. Using the generalized interpolation material point method for fluid-solid interactions induced by surface tension -- Chapter 5. Conclusions
Three-dimensional CFD simulations with large displacement of the geometries using a connectivity-change moving mesh approach
This paper deals with three-dimensional (3D) numerical simulations involving 3D moving geometries with large displacements on unstructured meshes. Such simulations are of great value to industry, but remain very time-consuming. A robust moving mesh algorithm coupling an elasticity-like mesh deformation solution and mesh optimizations was proposed in previous works, which removes the need for global remeshing when performing large displacements. The optimizations, and in particular generalized edge/face swapping, preserve the initial quality of the mesh throughout the simulation. We propose to integrate an Arbitrary Lagrangian Eulerian compressible flow solver into this process to demonstrate its capabilities in a full CFD computation context. This solver relies on a local enforcement of the discrete geometric conservation law to preserve the order of accuracy of the time integration. The displacement of the geometries is either imposed, or driven by fluid–structure interaction (FSI). In the latter case, the six degrees of freedom approach for rigid bodies is considered. Finally, several 3D imposed-motion and FSI examples are given to validate the proposed approach, both in academic and industrial configurations
Adaptive finite element simulation of three-dimensional surface tension dominated free-surface flow problems
An arbitrary Lagrangian--Eulerian finite element method is described for the solution of time-dependent, three-dimensional, free-surface flow problems. Many flows of practical significance involve contact lines, where the free surface meets a solid boundary. This contact line may be pinned to a particular part of the solid but is more typically free to slide in a manner that is characterised by the dynamic contact angle formed by the fluid. We focus on the latter case and use a model that admits spatial variation of the contact angle: thus permitting variable wetting properties to be simulated.
The problems are driven by the motion of the fluid free surface (under the action of surface tension and external forces such as gravity) hence the geometry evolves as part of the solution, and mesh adaptivity is required to maintain the quality of the computational mesh for the physical domain. Continuous mesh adaptivity, in the form of a pseudo-elastic mesh movement scheme, is used to move the interior mesh nodes in response to the motion of the fluid's free surface. Periodic, discrete remeshing stages are also used for cases in which the fluid volume has grown, or is sufficiently distorted, by the free-surface motion. Examples are given of a droplet sliding on an inclined uniform plane and of a droplet spreading on a surface with variable wetting properties
Two fluid space-time discontinuous Galerkin finite element method. Part I: numerical algorithm
A novel numerical method for two fluid flow computations is presented, which combines the space-time discontinuous Galerkin finite element discretization with the level set method and cut-cell based interface tracking. The space-time discontinuous Galerkin (STDG) finite element method offers high accuracy, an inherent ability to handle discontinuities and a very local stencil, making it relatively easy to combine with local {\it hp}-refinement. The front tracking is incorporated via cut-cell mesh refinement to ensure a sharp interface between the fluids. To compute the interface dynamics the level set method (LSM) is used because of its ability to deal with merging and breakup. Also, the LSM is easy to extend to higher dimensions. Small cells arising from the cut-cell refinement are merged to improve the stability and performance. The interface conditions are incorporated in the numerical flux at the interface and the STDG discretization ensures that the scheme is conservative as long as the numerical fluxes are conservative
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