Flux limiters

Flux limiters

A flux limiter is a numerical technique used to limit the value of the flux function F(u) in order to prevent numerical distortion and eliminate numerical oscillation in the numerical solutions of equations, particularly near discontinuities. The purpose of a flux limiter is to avoid unphysical oscillations and limit spurious growth in the grid averages.From: Adaptive Method of Lines [2019], Computational Fluid Dynamics for Incompressible Flows [2020], Eco-hydraulic Modelling of Eutrophication for Reservoir Management [2019]

Computational Heat Transfer

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Published in Greg F. Naterer, Advanced Heat Transfer, 2018

Greg F. Naterer

A high resolution method can be used for a numerical solution of differential equations where high accuracy is required to resolve small-scale phenomena such as shock waves and discontinuities. Second-order or higher accuracy is used to prevent spurious oscillations in the solutions. These methods use the concept of flux limiters, or slope limiting functions that have the effect of limiting the solution gradient near shock waves or discontinuities. In high-resolution methods, the number of mesh points containing a discontinuity is usually small compared with a first-order scheme of similar accuracy. Shu (2009) presented a review of high resolution schemes for convection dominated flows and applications in computational fluid dynamics.

Euler-Euler Model of Bubbly Flow Using Particle-Center-Averaging Method

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Published in Nuclear Science and Engineering, 2022

Hongmei Lyu, Fabian Schlegel, Roland Rzehak, Dirk Lucas

For the discretization of the convection terms, a flux limiter is used to make the simulations stable. A first-order Euler implicit scheme is used for temporal discretization. The first-order scheme is chosen because it is bounded and unconditionally stable.36 It is less accurate but can be more stable than the higher-order method.37,38 According to Seng et al.39 the Crank-Nicolson scheme, which is second order, may cause the numerical solution to have an oscillatory convergence. Similarly, for the discretization of the diffusion equations solved for the quantity conversions, a first-order Euler implicit scheme is used for the temporal discretization, and a Gauss linear scheme is used for the discretization of the Laplacian term.

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Computational Heat Transfer

Euler-Euler Model of Bubbly Flow Using Particle-Center-Averaging Method