High-order upwind residual distribution schemes on isoparametric curved elements

Residual distribution schemes are discussed in the context of higher order spatial discretization for hyperbolic conservation laws. The discrete solution is globally continuous, defined by a Finite Element space based on triangular Lagrangian Pk elements. A natural subtriangulation of these elements allows the reuse of simple distribution formula previously developed for linear P1 triangles. The paper introduces curved elements with piecewise quadratic approximation of the boundaries of the domain, using standard subor isoparametric transformation. Numerical results for the Euler equations confirm the predicted order of accuracy, showing the importance of a higher order approximation of the geometry.