7,131 research outputs found

    Using the generalized interpolation material point method for fluid-solid interactions induced by surface tension

    Get PDF
    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

    BPX-Preconditioning for isogeometric analysis

    Get PDF
    We consider elliptic PDEs (partial differential equations) in the framework of isogeometric analysis, i.e., we treat the physical domain by means of a B-spline or Nurbs mapping which we assume to be regular. The numerical solution of the PDE is computed by means of tensor product B-splines mapped onto the physical domain. We construct additive multilevel preconditioners and show that they are asymptotically optimal, i.e., the spectral condition number of the resulting preconditioned stiffness matrix is independent of hh. Together with a nested iteration scheme, this enables an iterative solution scheme of optimal linear complexity. The theoretical results are substantiated by numerical examples in two and three space dimensions

    Fast Isogeometric Boundary Element Method based on Independent Field Approximation

    Full text link
    An isogeometric boundary element method for problems in elasticity is presented, which is based on an independent approximation for the geometry, traction and displacement field. This enables a flexible choice of refinement strategies, permits an efficient evaluation of geometry related information, a mixed collocation scheme which deals with discontinuous tractions along non-smooth boundaries and a significant reduction of the right hand side of the system of equations for common boundary conditions. All these benefits are achieved without any loss of accuracy compared to conventional isogeometric formulations. The system matrices are approximated by means of hierarchical matrices to reduce the computational complexity for large scale analysis. For the required geometrical bisection of the domain, a strategy for the evaluation of bounding boxes containing the supports of NURBS basis functions is presented. The versatility and accuracy of the proposed methodology is demonstrated by convergence studies showing optimal rates and real world examples in two and three dimensions.Comment: 32 pages, 27 figure
    corecore