Nonlinearly stable flux reconstruction high-order methods in split form

The flux reconstruction (FR) method has gained popularity in the research community as it recovers promising high-order methods through modally filtered correction fields, such discontinuous Galerkin method, amongst others, on unstructured grids over complex geometries. Moreover, FR schemes, specifically energy stable (ESFR) schemes also known Vincent-Castonguay-Jameson-Huynh have proven attractive they allow for design flexibility well stability proofs linear advection problem affine elements. Additionally, split forms recently seen a resurgence activity due to their resultant nonlinear (entropy) proofs. This paper derives first time nonlinearly ESFR form that enable for, uncollocated, modal, with different volume and surface cubature nodes. critical enabling technology is applying splitting discrete stiffness operator. naturally leads appropriate numerical fluxes, both entropy conservation When these are recast strong form, differ from found literature functions incorporated integral. Furthermore, experiments conducted verifying new class of proposed contrast standard approach. Lastly, shown obtain correct orders accuracy.