Accelerated Piston Problem and High Order Moving Boundary Tracking Method for Compressible Fluid Flows

Du, Zhifang; Li, Jiequan

doi:10.1137/19m1266599

Cited by 9 publications

(9 citation statements)

References 30 publications

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“…𝑘=𝑎,𝑏 (𝜌𝜙 𝑘 𝑒 𝑘 ) 𝑛 𝑖 𝛾 𝑘 (𝜌𝑒) 𝑛 𝑖 by using (18), the mid-point value of the ratio of specific heats 𝛾…”

Section: Second-order Accurate Grp Extensionmentioning

confidence: 99%

“…However, it is difficult to maintain sharp material interfaces in Eulerian meshes. Even so, there are various ways to preserve the sharpness of material interfaces for Eulerian simulations, such as front-tracking methods, moving boundary tracking (MBT) methods [20,53,18], level-set methods [30,31,41] and interface reconstruction methods. Front-tracking methods take discontinuities (including material interfaces) as moving fronts and use an additional Lagrangian grid on the interfaces.…”

Section: Introductionmentioning

confidence: 99%

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An energy-splitting high order numerical method for multi-material flows

Lei¹,

Li²

2020

Preprint

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This chapter deals with multi-material flow problems by a kind of effective numerical methods, based on a series of reduced forms of the Baer-Nunziato (BN) model. Numerical simulations often face a host of difficult challenges, typically including the volume fraction positivity and stability of multi-material shocks. To cope with these challenges, we propose a new non-oscillatory energy-splitting Godunovtype scheme for computing multi-fluid flows in the Eulerian framework. A novel reduced version of the BN model is introduced as the basis for the energy-splitting scheme. In comparison with existing two-material compressible flow models obtained by reducing the BN model in the literature, it is shown that our new reduced model can simulate the kinetic energy exchange around material interfaces very effectively. Then a second-order accurate extension of the energy-splitting Godunov-type scheme is made using the generalized Riemann problem (GRP) solver. Numerical experiments are carried out for the shock-interface interaction, shock-bubble interaction and the Richtmyer-Meshkov instability problems, which demonstrate the excellent performance of this type of schemes.

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“…𝑘=𝑎,𝑏 (𝜌𝜙 𝑘 𝑒 𝑘 ) 𝑛 𝑖 𝛾 𝑘 (𝜌𝑒) 𝑛 𝑖 by using (18), the mid-point value of the ratio of specific heats 𝛾…”

Section: Second-order Accurate Grp Extensionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

An energy-splitting high order numerical method for multi-material flows

Lei¹,

Li²

2020

Preprint

Self Cite

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“…From the viewpoint of numerical analysis, it is questionable whether the numerical boundary conditions are compatible with the discretized governing equations even though the underlying PDE models are well-posed. Hence it is worth addressing issue even though there are lots of studies available [7,11,12,13,14,15,16,17,18,19,28,29,30].…”

Section: Introductionmentioning

confidence: 99%

“…In fact, for linear problems, physical boundary conditions depend on characteristic propagations. While for nonlinear compressible fluid flows, many physical boundary conditions are prescribed upon surroundings and cannot be even given a priori, such as the interaction of shock with solid boundaries [6] and the solid body floating in the air [13]. Numerically, situations become more complicated.…”

Section: Introductionmentioning

confidence: 99%

“…Such a study has two-fold goals: (i) It is used to the compatibility of prescribed boundary condition with the governing equations; (ii) It proposes a family of high order numerical boundary conditions effectively compatible with the discretized governing equations. In fact, accelerated piston problems [8,13] are the one-sided GRP formulated here and they have been refined to put into the simulation of fluid flows with moving boundaries [14,13]. In [12], the similar idea was employed if the flow is smooth and consistent with the inverse Lax-Wendroff method [29].…”

Section: Introductionmentioning

confidence: 99%

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One-sided GRP Solver and Numerical Boundary Conditions for compressible fluid flows

Li,

Zhang

2021

Preprint

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In the computation of compressible fluid flows, numerical boundary conditions are always necessary for all physical variables at computational boundaries while just partial physical variables are often prescribed as physical boundary conditions. Certain extrapolation technique or ghost cells are often employed traditionally for this issue but spurious wave reflections often arise to cause numerical instability. In this paper, we associate this issue with the one-sided generalized Riemann problem (GRP) solver motivated by the accelerated piston problem in gas dynamics so that the extrapolation technique can be actually avoided. In fact, the compatibility arguments naturally requires to formulate the one-sided generalized Riemann problem and incorporate it into the numerical procedure of boundary conditions. As far as the interaction of nonlinear waves with physical boundaries, such a one-sided GRP solver shows significant effects, as numerical experiments demonstrate, on avoiding spurious wave reflections at the computational boundaries.

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A monolithic arbitrary Lagrangian–Eulerian‐based finite element strategy for fluid–structure interaction problems involving a compressible fluid

Dutta

Jog

2021

Numerical Meth Engineering

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In this work, we present a new monolithic finite element strategy for solving fluid-structure interaction problems involving a compressible fluid and a hyperelastic structure. In the Lagrangian limit, the time-stepping strategy that we propose conserves the total energy, and linear and angular momenta. Detailed proofs with numerical validations are provided. We use a displacement-based Lagrangian formulation for the structure, and a velocity-based arbitrary Lagrangian-Eulerian mixed formulation with appropriately chosen interpolations for the various field variables to ensure stability of the resulting numerical procedure. A hybrid formulation is used to prevent locking of thin structures.Apart from physical variables such as displacement, velocity, and so forth, no new variables are introduced in the formulation. The use of the exact tangent stiffness matrix ensures that the algorithm converges quadratically within each time step. A number of benchmark examples have been solved to illustrate the good performance of the proposed method.

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Accelerated Piston Problem and High Order Moving Boundary Tracking Method for Compressible Fluid Flows

Cited by 9 publications

References 30 publications

An energy-splitting high order numerical method for multi-material flows

An energy-splitting high order numerical method for multi-material flows

One-sided GRP Solver and Numerical Boundary Conditions for compressible fluid flows

A monolithic arbitrary Lagrangian–Eulerian‐based finite element strategy for fluid–structure interaction problems involving a compressible fluid

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