A cell-centered implicit-explicit Lagrangian scheme for a unified model of nonlinear continuum mechanics on unstructured meshes

Boscheri, Walter; Chiocchetti, Simone; Peshkov, Ilya

doi:10.1016/j.jcp.2021.110852

Cited by 10 publications

(14 citation statements)

References 97 publications

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“…Although the column is shrinking at first, it "bounces off" at some point and starts to elongate. This effect was also observed in [4] and [19]. The blue line shows comparison to a finite element simulation (created using the Fenics software [23]).…”

Section: Twisting Columnmentioning

confidence: 52%

“…Three things can be tested in this benchmark. Firstly, we plot the coordinate of the central point, which we then compare to data from the finite volume simulation [4]. Figure 2 shows that we get a reasonable agreement.…”

Section: Beryllium Platementioning

confidence: 76%

“…The scheme is then tested on benchmarks like a vibrating Beryllium plate, twisting column, laminar Taylor-Couette flow, and lid-driven cavity flow, and shows acceptable agreement with the data, although finite volume and discontinuous Galerking ADER schemes [10,4] usually offer better precision.…”

Section: Discussionmentioning

confidence: 99%

“…For an elastic solid = ∞ and for a Newtonian fluid is a constant, while for non-Newtonian fluids and elastoplastic solids it should be taken as a function of [32,31]. With this new addition, the equation for is often stiff, and therefore, implicit and exponential time integrators are recommended [10,4]. However, we already have a very small time step in our explicit SHTC-SPH integrator (as opposed to fully implicit finite element or finite volume approaches), so for performance reasons, we use a simpler splitting strategy, using the classical RK4 scheme [20] for integrating the relaxation term in the PDE for :…”

Section: Adding Relaxationmentioning

confidence: 99%

“…Previously, the unified model of continuum mechanics was discretized using various mesh-based techniques including Godunov-type finite volume methods and Discontinuous Galerkin methods [10], Arbitrary Lagrangian Eulerian methods [31,7], a finite volume methods in the Updated Lagrangian formulation with a high-order IMEX time integrator [4], semi-implicit staggered finite volume method [5] for low-Mach problems, thermodynamically compatible finite volume scheme [8].…”

Section: Introductionmentioning

confidence: 99%

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Unified description of fluids and solids in Smoothed Particle Hydrodynamics

Kincl¹,

Peshkov²,

Pavelka³

et al. 2022

Preprint

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Smoothed Particle Hydrodynamics (SPH) methods are advantageous in simulations of fluids in domains with free boundary. Special SPH methods have also been developed to simulate solids. However, there are situations where the matter behaves partly as a fluid and partly as a solid, for instance, the solidification front in 3D printing, or any system involving both fluid and solid phases. We develop an SPH-like method that is suitable for both fluids and solids at the same time. Instead of the typical discretization of hydrodynamics, we discretize the Symmetric Hyperbolic Thermodynamically Compatible equations (SHTC), which describe both fluids, elastic solids, and visco-elasto-plastic solids within a single framework. The resulting SHTC-SPH method is then tested on various benchmarks from the hydrodynamics and dynamics of solids and shows remarkable agreement with the data.

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Section: Twisting Columnmentioning

confidence: 52%

Section: Beryllium Platementioning

confidence: 76%

Section: Discussionmentioning

confidence: 99%