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An efficient method for scalar advection is developed that selectively preserves monotonicity.
The moments method for scalar random variables seems to be very straightforward, however in general we have more complex situations.
In this paper we develop an unsplit, higher order Godunov method for scalar conservation laws in two dimensions.
The proposed method for scalar equation has been extended in a vector form to solve the system of quasi-linear hyperbolic pdes.
Lakoba, J. Yang, A generalized Petviashvili iteration method for scalar and vector Hamiltonian equations with arbitrary form of nonlinearity, J. Comput.
We also introduce a second-order, unsplit, volume-of-fluid advection algorithm that is based on a second-order, finite difference method for scalar conservation laws due to Bell, Dawson and Shubin.
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This paper presents preliminary developments of entropy-stable residual distribution methods for scalar problems.
In contrast to previously applied Lagrangian methods for scalar fields, the model presented here is shown to be applicable to inhomogeneous reacting liquid-phase flows.
Many one-dimensional experiments are performed based on SL-FV WENO 3 and WENO 5 reconstructions in order to validate the performance and efficiency of the proposed methods for scalar and conservation law systems.
This multivariate uncertainty method is an extension of classical uncertainty methods used for scalar variables and tracks the correlation between all variates along with the sample variance instead of just tracking the standard uncertainty.
The proposed method for a scalar equation is extended to solve the system of quasi-linear hyperbolic equations.
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