Finite element simulation of compressible particle-laden gas flows

Gurris, Marcel; Kuzmin, Dmitri; Turek, Stefan

doi:10.1016/j.cam.2009.07.041

Cited by 14 publications

(7 citation statements)

References 14 publications

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“…Either operator splitting techniques as presented in Section 5.1 and applied in [38] to stationary as well as non-stationary problems may be employed, or the equations may be integrated in time by the fully coupled implicit time integration as discussed in Chapter 5.2. At first glance, the former approach significantly reduces the computational costs since the arising algebraic systems can be solved separately.…”

Section: Operator Splitting Vs Fully Coupled Solution Strategymentioning

confidence: 99%

“…The restriction to one wave simplifies the solution of the boundary Riemann problem of the particulate phase. To avoid unphysical boundary layers [38], we use the same boundary Riemann solver as for the gas phase [38,9]. The flux formula of Roe is given by…”

Section: Inlet and Outlet Boundary Conditionsmentioning

confidence: 99%

“…As a starting point, we recall the operator splitting that was applied to the two-fluid model in [38]. In transient computations a time integration scheme of second or higher order is usually applied.…”

Section: Operator Splittingmentioning

confidence: 99%

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Implicit finite element schemes for stationary compressible particle-laden gas flows

Gurris

Kuzmin

Turek

2011

Journal of Computational and Applied Mathematics

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a b s t r a c tThe derivation of macroscopic models for particle-laden gas flows is reviewed. Semiimplicit and Newton-like finite element methods are developed for the stationary two-fluid model governing compressible particle-laden gas flows. The Galerkin discretization of the inviscid fluxes is potentially oscillatory and unstable. To suppress numerical oscillations, the spatial discretization is performed by a high-resolution finite element scheme based on algebraic flux correction. A multidimensional limiter of TVD type is employed. An important goal is the efficient computation of stationary solutions in a wide range of Mach numbers. This is a challenging task due to oscillatory correction factors associated with TVD-type flux limiters and the additional strong nonlinearity caused by interfacial coupling terms. A semi-implicit scheme is derived by a time-lagged linearization of the nonlinear residual, and a Newton-like method is obtained in the limit of infinite CFL numbers. The original Jacobian is replaced by a low-order approximation. Special emphasis is laid on the numerical treatment of weakly imposed boundary conditions. It is shown that the proposed approach offers unconditional stability and faster convergence rates for increasing CFL numbers. The strongly coupled solver is compared to operator splitting techniques, which are shown to be less robust.

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Section: Operator Splitting Vs Fully Coupled Solution Strategymentioning

confidence: 99%

Section: Inlet and Outlet Boundary Conditionsmentioning

confidence: 99%

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Implicit finite element schemes for stationary compressible particle-laden gas flows

Gurris

Kuzmin

Turek

2011

Journal of Computational and Applied Mathematics

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“…Recall that in real applications, the drag coefficient µ is not constant (depends on the Reynolds number of the particles). For physical applications with non-constant drag coefficient, we refer to [6,8,9,24]. Here we assume µ = 0.2 is constant.…”

Section: Riemann Problem Solution: Numerical Solutions Vs Theoretical...mentioning

confidence: 99%

Eulerian droplet model: Delta-shock waves and solution of the Riemann problem

Keita

Bourgault

2019

Journal of Mathematical Analysis and Applications

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We study an Eulerian droplet model which can be seen as the pressureless gas system with a source term, a subsystem of this model and the inviscid Burgers equation with source term. The condition for loss of regularity of a solution to Burgers equation with source term is established. The same condition applies to the Eulerian droplet model and its subsystem. The Riemann problem for the Eulerian droplet model is constructively solved by going through the solution of the Riemann problems for the inviscid Burgers equation with a source term and the subsystem, respectively. Under suitable generalized Rankine-Hugoniot relations and entropy condition, the existence of delta-shock solution is established. The existence of a solution to the generalized Rankine-Hugoniot conditions is proven. Some numerical illustrations are presented.

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“…Several numerical methods for dusty gas flow models can be found in, for example, [6,25,26,27,40,45,50,51]. However, efficiency, accuracy and resolution of these methods are limited due to strong singularities typically developed in the pressureless dusty fraction.…”

Section: Introductionmentioning

confidence: 99%

Hybrid Finite-Volume-Particle Method for Dusty Gas Flows

Chertock¹,

Cui²,

Kurganov³

2017

The SMAI Journal of Computational Mathematics

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Abstract. We first study the one-dimensional dusty gas flow modeled by the two-phase system composed of a gaseous carrier (gas phase) and a particulate suspended phase (dust phase). The gas phase is modeled by the compressible Euler equations of gas dynamics and the dust phase is modeled by the pressureless gas dynamics equations. These two sets of conservation laws are coupled through source terms that model momentum and heat transfers between the phases. When an Eulerian method is adopted for this model, one can notice the obtained numerical results are typically significantly affected by numerical diffusion. This phenomenon occurs since the pressureless gas equations are nonstrictly hyperbolic and have degenerate structure in which singular delta shocks are formed, and these strong singularities are vulnerable to the numerical diffusion.We introduce a low dissipative hybrid finite-volume-particle method in which the compressible Euler equations for the gas phase are solved by a central-upwind scheme, while the pressureless gas dynamics equations for the dust phase are solved by a sticky particle method. The obtained numerical results demonstrate that our hybrid method provides a sharp resolution even when a relatively small number of particle is used.We then extend the hybrid finite-volume-particle method to the three-dimensional dusty gas flows with axial symmetry. In the studied model, gravitational effects are taken into account. This brings an additional level of complexity to the development of the finite-volume-particle method since a delicate balance between the flux and gravitational source terms should be respected at the discrete level. We test the proposed method on a number of numerical examples including the one that models volcanic eruptions.Math. classification. 65M08, 76M12, 76M28, 86-08, 76M25, 35L65.

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Finite element simulation of compressible particle-laden gas flows

Cited by 14 publications

References 14 publications

Implicit finite element schemes for stationary compressible particle-laden gas flows

Implicit finite element schemes for stationary compressible particle-laden gas flows

Eulerian droplet model: Delta-shock waves and solution of the Riemann problem

Hybrid Finite-Volume-Particle Method for Dusty Gas Flows

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