644 research outputs found
Improving convergence in smoothed particle hydrodynamics simulations without pairing instability
The numerical convergence of smoothed particle hydrodynamics (SPH) can be
severely restricted by random force errors induced by particle disorder,
especially in shear flows, which are ubiquitous in astrophysics. The increase
in the number NH of neighbours when switching to more extended smoothing
kernels at fixed resolution (using an appropriate definition for the SPH
resolution scale) is insufficient to combat these errors. Consequently, trading
resolution for better convergence is necessary, but for traditional smoothing
kernels this option is limited by the pairing (or clumping) instability.
Therefore, we investigate the suitability of the Wendland functions as
smoothing kernels and compare them with the traditional B-splines. Linear
stability analysis in three dimensions and test simulations demonstrate that
the Wendland kernels avoid the pairing instability for all NH, despite having
vanishing derivative at the origin (disproving traditional ideas about the
origin of this instability; instead, we uncover a relation with the kernel
Fourier transform and give an explanation in terms of the SPH density
estimator). The Wendland kernels are computationally more convenient than the
higher-order B-splines, allowing large NH and hence better numerical
convergence (note that computational costs rise sub-linear with NH). Our
analysis also shows that at low NH the quartic spline kernel with NH ~= 60
obtains much better convergence then the standard cubic spline.Comment: substantially revised version, accepted for publication in MNRAS, 15
pages, 13 figure
An isogeometric analysis for elliptic homogenization problems
A novel and efficient approach which is based on the framework of
isogeometric analysis for elliptic homogenization problems is proposed. These
problems possess highly oscillating coefficients leading to extremely high
computational expenses while using traditional finite element methods. The
isogeometric analysis heterogeneous multiscale method (IGA-HMM) investigated in
this paper is regarded as an alternative approach to the standard Finite
Element Heterogeneous Multiscale Method (FE-HMM) which is currently an
effective framework to solve these problems. The method utilizes non-uniform
rational B-splines (NURBS) in both macro and micro levels instead of standard
Lagrange basis. Beside the ability to describe exactly the geometry, it
tremendously facilitates high-order macroscopic/microscopic discretizations
thanks to the flexibility of refinement and degree elevation with an arbitrary
continuity level provided by NURBS basis functions. A priori error estimates of
the discretization error coming from macro and micro meshes and optimal micro
refinement strategies for macro/micro NURBS basis functions of arbitrary orders
are derived. Numerical results show the excellent performance of the proposed
method
Isogeometric analysis applied to frictionless large deformation elastoplastic contact
This paper focuses on the application of isogeometric analysis to model frictionless large deformation contact between deformable bodies and rigid surfaces that may be represented by analytical functions. The contact constraints are satisfied exactly with the augmented Lagrangian method, and treated with a mortar-based approach combined with a simplified integration method to avoid segmentation of the contact surfaces. The spatial discretization of the deformable body is performed with NURBS and C0-continuous Lagrange polynomial elements. The numerical examples demonstrate that isogeometric surface discretization delivers more accurate and robust predictions of the response compared to Lagrange discretizations
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