High-order upwind residual distribution schemes on isoparametric curved elements

Residual distribution schemes on curved geometries are discussed in the context of higher order spatial discretization for hyperbolic conservation laws. The discrete solution, defined by a Finite Element space based on triangular Lagrangian Pk elements, is globally continuous. A natural sub-triangulation of these elements allows to reuse the simple distribution schemes previously developed for linear P1 triangles. The paper introduces curved elements with piecewise quadratic and cubic approximation of the boundaries of the domain, using standard sub- or 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.