High-Order Curvilinear Finite Element Methods for Lagrangian Hydrodynamics

Dobrev, Veselin; Kolev, Tzanio V.; Rieben, Robert N.

doi:10.1137/120864672

Cited by 198 publications

(186 citation statements)

References 31 publications

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“…(U n+1 +U n ) is used to preserve total energy from time t n to time t n+1 [7,8]. The pressure unknowns is computed directly by equation of state:…”

Section: Time Discretizationmentioning

confidence: 99%

A Lagrangian Finite Element Method for the Simulation of 3d Compressible Flows

Cremonesi¹,

Frangi²

2016

Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016)

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Abstract. The numerical solution of compressible fluid flows is of paramount importance in many industrial and engineering applications. Compared to the classical fluid dynamics, the introduction of the fluid compressibility changes the formulation of the problem and consequently its computational treatment.Among the possible numerical solutions of compressible flow problems, the finite element method has always been privileged. However, the standard Eulerian approaches with fixed domain are not particularly suited to represent the strong shock waves and the significant movement of the external boundaries. On the contrary, in problems characterized by evolving surfaces, Lagrangian approaches can be very effective.The governing equations of compressible flow problems are mass, momentum and energy conservation. These equations are discretized in the spirit of the Lagrangian Particle Finite Element Method (PFEM). The strong distortions of the mesh, typical of the Lagrangian approaches, are managed with a continuous remeshing of the computational domain. The nodal unknowns are velocities, density and internal energy. To fully exploit the potential of continuous remeshing, only nodal variables are stored and consequently only linear interpolation are used. In addition, an artificial viscosity has been introduced to stabilize the formation and propagation of shock waves. Finally, explicit time integration of the governing equations enables a highly efficient solution of the discretized problem.The proposed approach has been validated against typical benchmarks of gas dynamics in the presence of strong shock waves. A very good agreement has been shown in all the tests proving the excellent accuracy and versatility of the proposed method.

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“…(U n+1 +U n ) is used to preserve total energy from time t n to time t n+1 [7,8]. The pressure unknowns is computed directly by equation of state:…”

Section: Time Discretizationmentioning

confidence: 99%

A Lagrangian Finite Element Method for the Simulation of 3d Compressible Flows

Cremonesi¹,

Frangi²

2016

Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016)

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“…Capturing accurately the vorticity part is the difficult part of such simulation involving interacting shocks, rarefactions and contact waves. This problem is well known in Lagrangian and ALE community as it permits to qualitatively estimate the amount of numerical diffusion implied by the numerical method [86,40,42]. No exact solution does exist for this problem but one expects that high accurate numerical scheme may nicely capture the vortex motion.…”

Section: Numerical Experimentsmentioning

confidence: 99%

“…The 3D triple point problem [40,42] is constructed by considering the 2D setup from section 4.1.4 as a 2D axi-symmetric r, z setup, see Figure 7. Consequently subdomain #3 becomes an internal cylinder to cylindrical subdomain #2.…”

Section: D Mono-materials Triple Point Problemmentioning

confidence: 99%

“…Discontinuous Galerkin methods have also been applied to Lagrangian schemes in [61,59,60,79], while higher order finite element methods have been presented in [97,109,41,40,42] for solving the equations of Lagrangian hydrodynamics. The first high order Godunov-type Lagrangian finite volume schemes were proposed in [28,81], where a third order accurate essentially non-oscillatory (ENO) reconstruction operator has been employed on moving curved structured meshes.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Direct Arbitrary-Lagrangian–Eulerian ADER-MOOD finite volume schemes for multidimensional hyperbolic conservation laws

Boscheri

Loubère

Dumbser

2015

Journal of Computational Physics

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“…For example, Yu et al (2014) uses a flowdependent coefficient for the Laplacian. In Dobrev et al (2012), several tensor coefficient viscosity operators were considered, including a formulation in which directional viscosity coefficients were chosen to depend on directional length scales of a deformed Lagrangian volume. Here, we follow a similar approach, but the length scales come from the deformation of the elements, especially those in the grid transition region.…”

Section: Introductionmentioning

confidence: 99%

The spectral element method (SEM) on variable-resolution grids: evaluating grid sensitivity and resolution-aware numerical viscosity

et al. 2014

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Abstract. We evaluate the performance of the Community Atmosphere Model's (CAM) spectral element method on variable-resolution grids using the shallow-water equations in spherical geometry. We configure the method as it is used in CAM, with dissipation of grid scale variance, implemented using hyperviscosity. Hyperviscosity is highly scale selective and grid independent, but does require a resolutiondependent coefficient. For the spectral element method with variable-resolution grids and highly distorted elements, we obtain the best results if we introduce a tensor-based hyperviscosity with tensor coefficients tied to the eigenvalues of the local element metric tensor. The tensor hyperviscosity is constructed so that, for regions of uniform resolution, it matches the traditional constant-coefficient hyperviscosity. With the tensor hyperviscosity, the large-scale solution is almost completely unaffected by the presence of grid refinement. This later point is important for climate applications in which long term climatological averages can be imprinted by stationary inhomogeneities in the truncation error. We also evaluate the robustness of the approach with respect to grid quality by considering unstructured conforming quadrilateral grids generated with a well-known grid-generating toolkit and grids generated by SQuadGen, a new open source alternative which produces lower valence nodes.

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High-Order Curvilinear Finite Element Methods for Lagrangian Hydrodynamics

Cited by 198 publications

References 31 publications

A Lagrangian Finite Element Method for the Simulation of 3d Compressible Flows

A Lagrangian Finite Element Method for the Simulation of 3d Compressible Flows

Direct Arbitrary-Lagrangian–Eulerian ADER-MOOD finite volume schemes for multidimensional hyperbolic conservation laws

The spectral element method (SEM) on variable-resolution grids: evaluating grid sensitivity and resolution-aware numerical viscosity

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