Journal of Computational Physics
Journal of Computational Physics
On the rate of convergence to equilibrium for a system of conservation laws with a relaxation term
SIAM Journal on Mathematical Analysis
An Accurate and Robust Flux Splitting Scheme for Shock and Contact Discontinuities
SIAM Journal on Scientific Computing
Journal of Computational Physics
SIAM Journal on Numerical Analysis
Convergence of relaxation schemes for hyperbolic conservation laws with stiff source terms
Mathematics of Computation
The random projection method for hyperbolic conservation laws with stiff reaction terms
Journal of Computational Physics
Discrete Kinetic Schemes for Multidimensional Systems of Conservation Laws
SIAM Journal on Numerical Analysis
Relaxation approximation to bed-load sediment transport
Journal of Computational and Applied Mathematics
Toward a Mathematical Analysis for Drift-Flux Multiphase Flow Models in Networks
SIAM Journal on Scientific Computing
Mathematical models and methods in the water industry
Mathematical and Computer Modelling: An International Journal
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In this paper, we are interested in some basic investigations of properties of the relaxation schemes first introduced by Jin and Xin [1]. The main advantages of these schemes are that they neither require the use of Riemann solvers nor the computation of nonlinear flux Jacobians. This can be an important advantage when more complex models are considered where it is not possible to perform analytical calculations of Jacobians and/or when considering fluids with nonstandard equation of state. We apply the schemes (relaxing and relaxed) to a certain two-phase model where Jacobians cannot in general be calculated analytically. We first demonstrate that the original relaxation schemes of Jin and Xin produce a poor approximation for a typical mass transport example which involves transition from two-phase flow to single-phase flow. However, by introducing a slight modification of the original relaxation model by splitting the momentum flux into a mass and pressure part, we obtain some flux splitting relaxation schemes which for typical two-phase flow cases yield a more accurate and robust approximation.