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Both these procedures satisfy the C-property, the property of exactly preserving the quiescent flow.
The proposed scheme is capable of exactly preserving steady-state solutions expressed in terms of a nonlocal equilibrium variable.
Based on an analysis of the above hierarchy, attention is focussed on the development of a new implicit scheme using a positivity-preserving version of Toroet al.'s HLLC scheme, which is the simplest average-state solver capable of exactly preserving isolated shock, contact, and shear waves.
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The integrators exactly preserve energy and have arbitrarily high order.
We prove that this discretization exactly preserves the local mass and momentum.
In particular, the Hamiltonian can always be exactly preserved as a constant of the motion.
As the first step, a model system that exactly preserves the MHD hyperbolic singularities is considered.
First, it exactly preserves the LLG property of conserving the magnetization magnitude at each spatial location.
The new flux function exactly preserves the stationary contact discontinuity and does not capture the unphysical rarefaction shock.
The classic second-order averaged vector field (AVF) method can exactly preserve the energy for Hamiltonian systems.
A non-negativity preserving and well-balanced scheme that exactly preserves all the smooth steady states of the shallow water system, including the moving ones, is proposed.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com