Non-oscillatory central differencing for hyperbolic conservation laws
Journal of Computational Physics
Solution of the Cauchy problem for a conservation law with a discontinuous flux function
SIAM Journal on Mathematical Analysis
Nonlinear resonance in systems of conservation laws
SIAM Journal on Applied Mathematics
Analysis of a conservation PDE with discontinuous flux: a model of settler
SIAM Journal on Applied Mathematics
Convergence of the 2×2 Godunov method for a general resonant nonlinear balance law
SIAM Journal on Applied Mathematics
A mathematical model of traffic flow on a network of unidirectional roads
SIAM Journal on Mathematical Analysis
On scalar conservation laws with point source and discontinuous flux function
SIAM Journal on Mathematical Analysis
SIAM Journal on Numerical Analysis
Suppression of oscillations in Godunov's method for a resonant non-strictly hyperbolic system
SIAM Journal on Numerical Analysis
SIAM Journal on Applied Mathematics
A well-balanced scheme for the numerical processing of source terms in hyperbolic equations
SIAM Journal on Numerical Analysis
Dynamic and steady-state behavior of continuous sedimentation
SIAM Journal on Applied Mathematics
One-dimensional transport equations with discontinuous coefficients
Nonlinear Analysis: Theory, Methods & Applications
SIAM Journal on Applied Mathematics
Journal of Computational Physics
Mathematics of Computation
Extending viscosity solutions to Eikonal equations with discontinuous spatial dependence
Nonlinear Analysis: Theory, Methods & Applications
A Difference Scheme for Conservation Laws with a Discontinuous Flux: The Nonconvex Case
SIAM Journal on Numerical Analysis
Convergence of a Difference Scheme for Conservation Laws with a Discontinuous Flux
SIAM Journal on Numerical Analysis
SIAM Journal on Scientific Computing
Unconditionally stable methods for Hamilton--Jacobi equations
Journal of Computational Physics
A front tracking approach to a model of continuous sedimentation in ideal clarifier-thickener units
Nonlinear Analysis: Real World Applications
Monotone difference approximations for the simulation of clarifier-thickener units
Computing and Visualization in Science
Journal of Computational and Applied Mathematics
Mathematical and Computer Modelling: An International Journal
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In this paper, two existing one-dimensional mathematical models, one for continuous sedimentation of monodisperse suspensions and one for settling of polydisperse suspensions, are combined into a model of continuous separation of polydisperse mixtures. This model can be written as a first-order system of conservation laws for the local concentrations of each particle species with a flux vector that depends discontinuously on the space variable. This application motivates the extension of the Kurganov-Tadmor central difference scheme to systems with discontinuous flux. The new central schemes are based on discretizing an enlarged system in which the discontinuous coefficients are viewed as additional conservation laws. These additional conservation laws can either be discretized and the evolution of the discontinuity parameters is calculated in each time step, or solved exactly, that is, the discontinuity parameters are kept constant (with respect to time). Numerical examples and an L1 error study show that the Kurganov-Tadmor scheme with first-order in time discretization produces spurious oscillations, whereas its semi-discrete version, discretized by a second-order Runge-Kutta scheme, produces good results. The scheme with discontinuity parameters kept constant is slightly more accurate than when these are evolved. Numerical examples illustrate the application to separation of polydisperse suspensions.