# A Fully Mass and Volume Conserving Implementation of a Characteristic Method for Transport Problems

@article{Arbogast2006AFM, title={A Fully Mass and Volume Conserving Implementation of a Characteristic Method for Transport Problems}, author={Todd Arbogast and Chieh-Sen Huang}, journal={SIAM J. Sci. Comput.}, year={2006}, volume={28}, pages={2001-2022} }

The characteristics-mixed method considers the transport not of a single point or fluid particle, but rather the mass in an entire region of fluid. This mass is transported along the characteristic curves of the hyperbolic part of the transport equation, and the scheme thereby produces very little numerical dispersion, conserves mass locally, and can use long time steps. However, since the shape of a characteristic trace-back region must be approximated in numerical implementation, its volume…

## 47 Citations

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An Eulerian--Lagrangian numerical approximation for a system of two conservation laws in one space dimension modeling a simplified two-phase flow problem in a porous medium is developed.

### Convergence of a Fully Conservative Volume Corrected Characteristic Method for Transport Problems

- MathematicsSIAM J. Numer. Anal.
- 2010

It is proved that the volume corrected method, with no diffusion term, gives a lower order $L^1$-convergence rate of $\mathcal{O}(h/\sqrt{\Delta t}+h+(\Delta t)^r)$, where $r$ is related to the accuracy of the characteristic tracing.

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- 2014

It is proved that the $L^2$ error bound the characteristic time-discrete system of the fully discrete method of characteristics to the time- Discrete system is $\tau$-independent and the numerical solution is bounded in $W^{1,\infty}$-norm unconditionally.

### AN EULERIAN-LAGRANGIAN WENO SCHEME FOR NONLINEAR CONSERVATION LAWS

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We develop a formally high order Eulerian-Lagrangian WENO finite volume scheme for nonlinear scalar conservation laws that combines ideas of Lagrangian traceline methods with WENO reconstructions.…

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- 2017

The scheme proposed in the paper generates comparable solutions with that of WENOJS, but with less CPU time, and the high-order spatial discretization is chosen to be the classical 5th-order weighted essentially non-oscillatory spatial interpolation.

### An Implicit Eulerian–Lagrangian WENO3 Scheme for Nonlinear Conservation Laws

- Computer ScienceJ. Sci. Comput.
- 2018

A new, formally third order, implicit Weighted Essentially Non-Oscillatory (iWENO3) finite volume scheme for solving systems of nonlinear conservation laws and a new Roe solver for the Euler system is developed to account for the Lagrangian tracings, which could be useful even for explicit EL-WenO schemes.

### Stability, Monotonicity, Maximum and Minimum Principles, and Implementation of the Volume Corrected Characteristic Method

- MathematicsSIAM J. Sci. Comput.
- 2011

The volume correction adjustment is important for stability and necessary for the monotonicity and the maximum and minimum principles of the method and a relatively weaker stability property is derived for the uncorrected characteristic-mixed method (CMM).

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