Approximate Riemann solver for compressible liquid vapor flow with phase transition and surface tension

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The Riemann problem is one of the basic building blocks for numerical methods in computational fluid mechanics. Nonetheless, there are still open questions and gaps in theory and modelling for situations with complex thermodynamic behavior. In this series, we compare numerical solutions of the macroscopic flow equations with molecular dynamics simulation data. To enable molecular dynamics for sufficiently large scales in time and space, we selected the truncated and shifted Lennard-Jones potential, for which also highly accurate equations of state are available. A comparison of a two-phase Riemann problem is shown, which involves a liquid and a vapor phase, with an undergoing phase transition. The loss of hyperbolicity allows for the occurrence of anomalous wave structures. We successfully compare the molecular dynamics data with two macroscopic numerical solutions obtained by either assuming local phase equilibrium or by imposing a kinetic relation and allowing for metastable states.

“…For this study, the method of Fechter et al [29,31,32] was simplified to a one-dimensional front-tracking scheme. In the bulk phases, the solution was obtained by the DGSEM solver FLEXI .…”

Section: Sharp Interface Ghost Fluid Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Comparison of macro- and microscopic solutions of the Riemann problem II. Two-phase shock tube

Hitz

Jöns

Heinen

et al. 2021

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“…For this study, the method of Fechter et al [16,18,19] was simplified to a one-dimensional front-tracking scheme. In the bulk phases, the solution was obtained by the DGSEM solver FLEXI .…”

Section: Sharp Interface Ghost Fluid Methodsmentioning

confidence: 99%

Comparison of macro- and microscopic solutions of the Riemann problem I. Supercritical shock tube and expansion into vacuum

Hitz

Heinen

Vrabec

et al. 2020

Self Cite

The Riemann problem is one of the basic building blocks for numerical methods in computational fluid mechanics. Nonetheless, there are still open questions and gaps in theory and modelling for situations with complex thermodynamic behavior. In this series, we compare numerical solutions of the macroscopic flow equations with molecular dynamics simulation data. To enable molecular dynamics for sufficiently large scales in time and space, we selected the truncated and shifted Lennard-Jones potential for which also highly accurate equations of state are available. A comparison of a twophase Riemann problem is shown, which involves a liquid and a vapor phase, with an undergoing phase transition. The loss of hyperbolicity allows for the occurrence of anomalous wave structures. We successfully compare the molecular dynamics data with two macroscopic numerical solutions obtained by either assuming local phase equilibrium or by imposing a kinetic relation and allowing for metastable states.

“…Consequently, it is important to resolve it accurately in numerical simulations. This can be achieved by using front-tracking algorithms such as the ghost-uid method [11,10], or front-capturing algorithms such as moving mesh methods [6]. For each of these numerical algorithms it is essential to describe the dynamics of the wave of interest precisely.…”

Section: Problem Descriptionmentioning

confidence: 99%

“…where α wd ≥ 0 is a tunable hyper-parameter that controls the amount of weight decay. Typically, one chooses p = 1 (to induce sparsity) or p = 2 as the exponent in (10). In this work, weight decay is observed for all layers except the output layer.…”

Section: Neural Networkmentioning

confidence: 99%

Constraint-aware neural networks for Riemann problems

Magiera

Ray

Hesthaven

et al. 2020

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Neural networks are increasingly used in complex (data-driven) simulations as surrogates or for accelerating the computation of classical surrogates. In many applications physical constraints, such as mass or energy conservation, must be satis ed to obtain reliable results. However, standard machine learning algorithms are generally not tailored to respect such constraints. We propose two di erent strategies to generate constraint-aware neural networks. We test their performance in the context of front-capturing schemes for strongly nonlinear wave motion in compressible uid ow. Precisely, in this context so-called Riemann problems have to be solved as surrogates. Their solution describes the local dynamics of the captured wave front in numerical simulations. Three model problems are considered: a cubic ux model problem, an isothermal two-phase ow model, and the Euler equations. We demonstrate that a decrease in the constraint deviation correlates with low discretization errors for all model problems, in addition to the structural advantage of ful lling the constraint.