Particle transport method for convection problems with reaction and diffusion

Shipilova, Olga; Haario, Heikki; Smolianski, Anton

doi:10.1002/fld.1438

Cited by 13 publications

(8 citation statements)

References 30 publications

(42 reference statements)

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“…Moreover, the Eulerian FEM requires discrete physical information not only at the nodes but also at the Gaussian points to initialize the system (9). Therefore, in the following we define the necessary particle-to-grid and node-to-particle interpolation techniques.…”

Section: Interpolation Techniquesmentioning

confidence: 99%

“…The transfer of information is commonly achieved by interpolation or projection techniques (e.g. global vs local information, damped least-squares, etc, [9], [10]), which are generally problem-dependent and require careful design, as seemingly small errors during the interpolation process can accumulate rapidly due to the large number of interpolations performed during a typical simulation [11]. Also, while splitting the physical operators facilitates the implementation of different solvers within the numerical scheme (lending itself to parallel computing), and greatly simplifies the numerical procedure, traditional splitting techniques are typically unable to achieve high-order accuracy (i.e.…”

Section: Introductionmentioning

confidence: 99%

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A Lagrangian–Eulerian finite element algorithm for advection–diffusion–reaction problems with phase change

Oliveira

Afonso

Zlotnik

2016

Computer Methods in Applied Mechanics and Engineering

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This paper presents a particle-based Lagrangian-Eulerian algorithm for the solution of the unsteady advectiondiffusion-reaction heat transfer equation with phase change. The algorithm combines a Lagrangian formulation for the advection + reaction problem with the Eulerian-based heat source method for the diffusion + phase change problem. The coupling between the Lagrangian and Eulerian subproblems is achieved with a phase change detector scheme based on a local latent heat balance and a consistent/conservative interpolation technique between Lagrangian particles and the Eulerian grid. This technique makes use of an auxiliary (finer) Eulerian grid that provides a simple and efficient method of tracking internal heterogeneities (e.g. phase boundaries), allows the use of higher order integration quadratures, and facilitates the implementation of multiscale techniques. The performance of the proposed algorithm is compared against one-and two-dimensional benchmark problems, i.e. pure rigid-body advection, isothermal and non-isothermal phase change, two-phase advective heat transfer and chemical reactions coupled with diffusion and advection. The numerical results confirm that the proposed solution method is accurate, oscillation-free and useful for and applicable to a wide range of fully coupled problems in science and engineering.

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Section: Interpolation Techniquesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Lagrangian–Eulerian finite element algorithm for advection–diffusion–reaction problems with phase change

Oliveira

Afonso

Zlotnik

2016

Computer Methods in Applied Mechanics and Engineering

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“…Boundary conditions of f = 0 were applied to the 'west' and 'south' boundaries, while ∂ f ∂n = 0 was applied to the remaining boundaries. The initial conditions were given by problem has the analytical solution [9] f = σ 0 f 0…”

Section: Propagation Of a Gaussian Pulsementioning

confidence: 99%

A singularity-avoiding moving least squares scheme for two-dimensional unstructured meshes

Chenoweth

Soria

Ooi

2009

Journal of Computational Physics

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Moving least squares interpolation schemes are in widespread use as a tool for numerical analysis on scattered data. In particular, they are often employed when solving partial differential equations on unstructured meshes, which are typically needed when the geometry defining the domain is complex. It is known that such schemes can be singular if the data points in the stencil happen to be in certain special geometric arrangements, however little research has addressed this issue specifically. In this paper, a moving least squares scheme is presented which is an appropriate tool for use when solving partial differential equations in two dimensions, and the precise conditions under which singularities occur are identified. The theory is then applied in the form of a stencil building algorithm which automatically detects singular stencils and corrects them in an efficient manner, while attempting to maintain stencil symmetry as closely as possible. Finally, the scheme is used in a convection-diffusion equation solver, and the results of a number of simulations are presented.

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“…The LE method takes advantage of appropriate operator splitting techniques to solve different aspects of the physical model with most suitable Lagrangian or Eulerian formalism [24] . Shipilova et al [25] applied a LE method (the particle transform method) to solve the convection-diffusion-reaction problems, numerical results showed that the PTM can avoid the numerical oscillation even for a very sparse grid. So far, there is no attempt to use the LE approaches to deal with the spurious numerical propagation phenomenon generated in simulating the reacting flows.…”

Section: Introductionmentioning

confidence: 99%

The dual information preserving method for stiff reacting flows

et al. 2017

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a b s t r a c tIn this paper, we construct a new numerical method to solve the reactive Euler equations to cure the numerical stiffness problem. The species mass equations are first decoupled from the reactive Euler equations, and then they are further fractionated into the convection step and the reaction step. In the convection step, by introducing two kinds of Lagrangian points (cell-point and particle-point), a dual information preserving (DIP) method is proposed to resolve the convection characteristics. In this new method, the information (including the transport value and the relative coordinates to the center of the current cell) of the cell-point and that of the particle-point are updated according to the velocity field. The information of the cell-point in a cell can effectively restrict the incorrect reaction activation caused by the numerical dissipation, while the information of the particle-point can help to preserve the sharp shock front once the strong shock waves are formed. Hence, by using the DIP method, the spurious numerical propagation phenomenon in stiff reacting flows is effectively eliminated. In addition, a numerical perturbation method is also developed to solve the fractional reaction step (ODE equation) to improve the stability and efficiency. A series of numerical examples are presented to validate the accuracy and robustness of the new method.

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Particle transport method for convection problems with reaction and diffusion

Cited by 13 publications

References 30 publications

A Lagrangian–Eulerian finite element algorithm for advection–diffusion–reaction problems with phase change

A Lagrangian–Eulerian finite element algorithm for advection–diffusion–reaction problems with phase change

A singularity-avoiding moving least squares scheme for two-dimensional unstructured meshes

The dual information preserving method for stiff reacting flows

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