173 research outputs found

    A Mixed Method for Axisymmetric Div-Curl Systems

    Get PDF
    We present a mixed method for a three-dimensional axisymmetric div-curl system reduced to a two-dimensional computational domain via cylindrical coordinates. We show that when the meridian axisymmetric Maxwell problem is approximated by a mixed method using the lowest order Nédélec elements (for the vector variable) and linear elements (for the Lagrange multiplier), one obtains optimal error estimates in certain weighted Sobolev norms. The main ingredient of the analysis is a sequence of projectors in the weighted norms satisfying some commutativity properties

    Developments and trends in three-dimensional mesh generation

    Get PDF
    An intense research effort over the last few years has produced several competing and apparently diverse methods for generating meshes. Recent progress is reviewed and the central themes are emphasized which form a solid foundation for future developments in mesh generation

    A single-domain spectral method for black hole puncture data

    Full text link
    We calculate puncture initial data corresponding to both single and binary black hole solutions of the constraint equations by means of a pseudo-spectral method applied in a single spatial domain. Introducing appropriate coordinates, these methods exhibit rapid convergence of the conformal factor and lead to highly accurate solutions. As an application we investigate small mass ratios of binary black holes and compare these with the corresponding test mass limit that we obtain through a semi-analytical limiting procedure. In particular, we compare the binding energy of puncture data in this limit with that of a test particle in the Schwarzschild spacetime and find that it deviates by 50% from the Schwarzschild result at the innermost stable circular orbit of Schwarzschild, if the ADM mass at each puncture is used to define the local black hole masses.Comment: 13 pages, 6 figures; published version with one important change, see Fig. 4 and the corresponding changes to the tex

    A Computational Framework for Axisymmetric Linear Elasticity and Parallel Iterative Solvers for Two-Phase Navier–Stokes

    Get PDF
    This dissertation explores ways to improve the computational efficiency of linear elasticity and the variable density/viscosity Navier--Stokes equations. While the approaches explored for these two problems are much different in nature, the end goal is the same - to reduce the computational effort required to form reliable numerical approximations.\\ The first topic considered is the axisymmetric linear elasticity problem. While the linear elasticity problem has been studied extensively in the finite-element literature, to the author\u27s knowledge, this is the first study of the elasticity problem in an axisymmetric setting. Indeed, the axisymmetric nature of the problem means that a change of variables to cylindrical coordinates reduces a three-dimensional problem into a decoupled one-dimensional and two-dimensional problem. The change of variables to cylindrical coordinates, however, affects the functional form of the divergence operator and the definition of the inner products. To develop a computational framework for the linear elasticity problem in this context, a new projection operator is defined that is tailored to the cylindrical form of the divergence and inner products. Using this framework, a stable finite-element quadruple is derived for k=1,2k=1,2. These computational rates are then validated with a few computational examples.\\ The second topic addressed in this work is the development of a new Schur complement approach for preconditioning the two-phase Navier--Stokes equations. Considerable research effort has been invested in the development of Schur complement preconditioning techniques for the Navier--Stokes equations, with the pressure-convection diffusion (PCD) operator and the least-squares commutator being among the most popular. Furthermore, more recently researchers have begun examining preconditioning strategies for variable density / viscosity Stokes and Navier--Stokes equations. This work contributes to recent work that has extended the PCD Schur complement approach for single phase flow to the variable phase case. Specifically, this work studies the effectiveness of a new two-phase PCD operator when applied to dynamic two-phase simulations that use the two-phase Navier--Stokes equations. To demonstrate the new two-phase PCD operators effectiveness, results are presented for standard benchmark problems, as well as parallel scaling results are presented for large-scale dynamic simulations for three-dimensional problems

    Mini-Workshop: Interface Problems in Computational Fluid Dynamics

    Get PDF
    Multiple difficulties are encountered when designing algorithms to simulate flows having free surfaces, embedded particles, or elastic containers. One difficulty common to all of these problems is that the associated interfaces are Lagrangian in character, while the fluid equations are naturally posed in the Eulerian frame. This workshop explores different approaches and algorithms developed to resolve these issues
    • …
    corecore