Accurate interface-tracking for arbitrary Lagrangian–Eulerian schemes

Bjøntegaard, Tormod; Rønquist, Einar M.

doi:10.1016/j.jcp.2009.03.012

Cited by 7 publications

(14 citation statements)

References 24 publications

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“…One such algorithm has been suggested in [25]. In order to be able to even evaluate the quality of such algorithms, work must be done in finding the optimal polynomial representation of a given parametric surface or parametric curve.…”

Section: Discussionmentioning

confidence: 99%

“…Retaining an optimal mesh in an evolutionary geometry is a very complicated and generally unsolved problem [25]. It makes it even more difficult that the problem of optimal representation of a given stationary parametric surface remains unsolved.…”

Section: Mesh Update Algorithmsmentioning

confidence: 99%

“…It is implemented by finding the unit normal vector at each mesh point (numerically) and then project the update ∆φ n+1 onto these vectors. The algorithm is also discussed in [25]. The third algorithm is specifically designed for our test case.…”

Section: Mesh Update Algorithmsmentioning

confidence: 99%

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High order numerical approximation of minimal surfaces

Tråsdahl¹,

Rønquist²

2011

Journal of Computational Physics

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We present an algorithm for finding high order numerical approximations of minimal surfaces with a fixed boundary. The algorithm employs parametrization by high order polynomials and a linearization of the weak formulation of the Laplace-Beltrami operator to arrive at an iterative procedure to evolve from a given initial surface to the final minimal surface. For the steady state solution we measure the approximation error in a case where the exact solution is known (the catenoid). In the framework of parametric interpolation, the choice of interpolation points (mesh nodes) is directly affecting the approximation error, and we discuss how to best update the mesh on the evolutionary surface such that the parametrization remains smooth. In our test case we achieve exponential convergence in the approximation of the minimal surface as the polynomial degree increases, but the rate of convergence greatly differs with different choices of mesh update algorithms.

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Section: Discussionmentioning

confidence: 99%

Section: Mesh Update Algorithmsmentioning

confidence: 99%

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High order numerical approximation of minimal surfaces

Tråsdahl¹,

Rønquist²

2011

Journal of Computational Physics

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“…With ''good position'' we mean that the collection of grid nodes, which are moved in this fashion, on each element at time t nþ1 should make the mapping from the reference domain to the physical domain as smooth as possible. In order to move a particle through a Lagrangian motion we need to integrate (1). Hence, in the case of using a multi-step time integrator, we need information about the velocity of a given fluid particle at different time-levels in order to achieve higher than first order accuracy.…”

Section: New Strategymentioning

confidence: 99%

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a b s t r a c tWe extend the computational method presented in [1] for tracking an interface immersed in a given velocity field to three spatial dimensions. The proposed method is particularly relevant to the simulation of unsteady free surface problems using the arbitrary Lagrangian-Eulerian framework, and has been constructed with two goals in mind: (i) to be able to accurately follow the interface; and (ii) to automatically maintain a good distribution of the grid points along the interface.

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confidence: 99%

Accurate interface-tracking of surfaces in three dimensions for arbitrary Lagrangian–Eulerian schemes

Bjøntegaard¹,

Rønquist²

2012

Journal of Computational Physics

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A Mixed Eulerian–Lagrangian Spectral Element Method for Nonlinear Wave Interaction with Fixed Structures

2019

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We present a high-order nodal spectral element method for the two-dimensional simulation of nonlinear water waves. The model is based on the mixed Eulerian-Lagrangian (MEL) method. Wave interaction with fixed truncated structures is handled using unstructured meshes consisting of high-order iso-parametric quadrilateral/triangular elements to represent the body surfaces as well as the free surface elevation. A numerical eigenvalue analysis highlights that using a thin top layer of quadrilateral elements circumvents the general instability problem associated with the use of asymmetric mesh topology. We demonstrate how to obtain a robust MEL scheme for highly nonlinear waves using an efficient combination of (i) global L 2 projection without quadrature errors, (ii) mild modal filtering and (iii) a combination of local and global re-meshing techniques. Numerical experiments for strongly nonlinear waves are presented. The experiments demonstrate that the spectral element model provides excellent accuracy in prediction of nonlinear and dispersive wave propagation. The model is also shown to accurately capture the interaction between solitary waves and fixed submerged and surface-piercing bodies. The wave motion and the wave-induced loads compare well to experimental and computational results from the literature. Keywords Nonlinear and dispersive free surface waves • Wave-structure interaction • Fully nonlinear potential flow • Spectral element method • Mixed Eulerian-Lagrangian • Marine hydrodynamics • Numerical wave tank B Carlos Monteserin

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Accurate interface-tracking for arbitrary Lagrangian–Eulerian schemes

Cited by 7 publications

References 24 publications

High order numerical approximation of minimal surfaces

High order numerical approximation of minimal surfaces

Accurate interface-tracking of surfaces in three dimensions for arbitrary Lagrangian–Eulerian schemes

A Mixed Eulerian–Lagrangian Spectral Element Method for Nonlinear Wave Interaction with Fixed Structures

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