We show how to combine in a natural way (i.e. without any test nor switch) the conservative and non conservative formulations of an hyperbolic system that has a conservative form. This is inspired from two different class of schemes: the Residual Distribution one  , and the Active Flux formulations  . This new class of scheme is proved to satisfy a Lax-Wendroff like theorem. We also develop a method to perform non linear stability. We illustrate the behaviour on several benchmarks, some quite challenging.
We show how to combine in a natural way (i.e. without any test nor switch) the conservative and non conservative formulations of an hyperbolic system that has a conservative form. This is inspired from two different class of schemes: the Residual Distribution one \mbox{%DIFAUXCMD MR4090481 , and the Active Flux formulations \mbox{%DIFAUXCMD AF1, AF3, AF4,AF5,RoeAF . This new class of scheme is proved to satisfy a Lax-Wendroff like theorem. We also develop a method to perform non linear stability. We illustrate the behaviour on several benchmarks, some quite challenging.
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\mbox{%DIFAUXCMD MR4090481
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\mbox{%DIFAUXCMD AF1, AF3, AF4,AF5,RoeAF