Lagrangian shock hydrodynamics on tetrahedral meshes: A stable and accurate variational multiscale approach

Scovazzi, Guglielmo

doi:10.1016/j.jcp.2012.06.033

Cited by 87 publications

(93 citation statements)

References 38 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…To this end, a comprehensive list of numerical examples in one, two and three dimensions has been presented. The overall methodology shows excellent behaviour in both shock-related hydrodynamics problems [55,89,[96][97][98] and bending dominated nearly incompressible solids. …”

Section: Discussionmentioning

confidence: 99%

“…This example was first presented in [88] and later used by many authors [55,60,89]. The example is designed to assess the shock capturing capabilities of the method.…”

Section: One Dimensional Sod Shock Tubementioning

confidence: 99%

“…More recently, the p-F formulation was improved in [5] for the case of nearly incompressible materials, by means of an additional conservation law for the Jacobian of the deformation J (widely known as volume map conservation law [42,[54][55][56][57]), providing extra flexibility for the calculation of the volumetric stress. This innovative idea extended the range of use of the formulation to nearly and fully incompressible media.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

An upwind vertex centred Finite Volume solver for Lagrangian solid dynamics

Aguirre

Gil

Bonet

et al. 2015

Journal of Computational Physics

152

View full text Add to dashboard Cite

A vertex centred Jameson-Schmidt-Turkel (JST) finite volume algorithm was recently introduced by the authors (Aguirre et al., 2014 [1]) in the context of fast solid isothermal dynamics. The spatial discretisation scheme was constructed upon a Lagrangian two-field mixed (linear momentum and the deformation gradient) formulation presented as a system of conservation laws [2][3][4]. In this paper, the formulation is further enhanced by introducing a novel upwind vertex centred finite volume algorithm with three key novelties. First, a conservation law for the volume map is incorporated into the existing two-field system to extend the range of applications towards the incompressibility limit (Gil et al., 2014 [5]). Second, the use of a linearised Riemann solver and reconstruction limiters is derived for the stabilisation of the scheme together with an efficient edge-based implementation. Third, the treatment of thermo-mechanical processes through a Mie-Grüneisen equation of state is incorporated in the proposed formulation. For completeness, the study of the eigenvalue structure of the resulting system of conservation laws is carried out to demonstrate hyperbolicity and obtain the correct time step bounds for non-isothermal processes. A series of numerical examples are presented in order to assess the robustness of the proposed methodology. The overall scheme shows excellent behaviour in shock and bending dominated nearly incompressible scenarios without spurious pressure oscillations, yielding second order of convergence for both velocities and stresses.

show abstract

Section: Discussionmentioning

confidence: 99%

“…This example was first presented in [88] and later used by many authors [55,60,89]. The example is designed to assess the shock capturing capabilities of the method.…”

Section: One Dimensional Sod Shock Tubementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

An upwind vertex centred Finite Volume solver for Lagrangian solid dynamics

Aguirre

Gil

Bonet

et al. 2015

Journal of Computational Physics

152

View full text Add to dashboard Cite

show abstract

“…Such techniques were also shown to provide an accuracy advantage when used in application to compressible problems (see e.g. [6]) A different mixed formulation is employed here with the goal of improving the accuracy of the Finite Element discretization. The idea is to combine different primary variables, in our case displacements and strains, following the concept described in [7].…”

Section: Introductionmentioning

confidence: 99%

Explicit mixed strain-displacement finite element for dynamic geometrically non-linear solid mechanics

et al. 2015

View full text Add to dashboard Cite

Aquesta és una còpia de la versió author's final draft d'un article publicat a la revista Computational mechanics. Although appealing for their simplicity, low-order finite elements face inherent limitations related to their poor convergence properties. Such difficulties typically manifest as mesh-dependent or excessively stiff behaviour when dealing with complex problems. A recent proposal to address such limitations is the adoption of mixed displacement-strain technologies which were shown to satisfactorily address both problems. Unfortunately, although appealing, the use of such element technology puts a large burden on the linear algebra, as the solution of larger linear systems is needed. In this paper, the use of an explicit time integration scheme for the solution of the mixed strain-displacement problem is explored as an alternative. An algorithm is devised to allow the effective time integration of the mixed problem. The developed method retains second order accuracy in time and is competitive in terms of computational cost with the standard irreducible formulation.

show abstract

“…Based on the idea of limiters, Boris and Book [3] developed the Flux Corrected Transport (FCT) and Löhner et al [26] extended this scheme to unstructured meshes in the FEM. Recently, the so-called variational multiscale (VMS) method, originally introduced by Hughes [19] has been successfully applied to derive stabilized finite element formulations for flow problems [14,20,[40][41][42][43][44]. Based on the finite volume (FV) scheme and following the idea of artificial diffusion, an important numerical improvement was conducted by Jameson et al [22] using a series of second and fourth order stabilization methods.…”

Section: Introductionmentioning

confidence: 99%

An implicit stabilized finite element method for the compressible Navier–Stokes equations using finite calculus

Kouhi

Oñate

2015

Comput Mech

View full text Add to dashboard Cite

A new implicit stabilized formulation for the numerical solution of the compressible NavierStokes equations is presented. The method is based on the Finite Calculus (FIC) scheme using the Galerkin finite element method (FEM) on triangular grids. Via the FIC formulation, two stabilization terms, called streamline term and transverse term, are added to the original conservation equations in the space-time domain. The non-linear system of equations resulting from the spatial discretization is solved implicitly using a damped Newton method benefiting from the exact Jacobian matrix. The matrix system is solved at each iteration with a preconditioned GMRES method. The efficiency of the proposed stabilization technique is checked out in the solution of 2D inviscid and laminar viscous flow problems where appropriate solutions are obtained especially near the boundary layer and shock waves. The work presented here can be considered as a follow up of a previous work of the authors [24]. In that paper, the stabilized Galerkin FEM based on the FIC formulation was derived for the Euler equations together with an explicit scheme. In the present paper, the extension of this work to the Navier-Stokes equations using an implicit scheme is presented.

show abstract

Lagrangian shock hydrodynamics on tetrahedral meshes: A stable and accurate variational multiscale approach

Cited by 87 publications

References 38 publications

An upwind vertex centred Finite Volume solver for Lagrangian solid dynamics

An upwind vertex centred Finite Volume solver for Lagrangian solid dynamics

Explicit mixed strain-displacement finite element for dynamic geometrically non-linear solid mechanics

An implicit stabilized finite element method for the compressible Navier–Stokes equations using finite calculus

Contact Info

Product

Resources

About