High-order accurate discontinuous finite element solution of the 2D Euler equations
Journal of Computational Physics
Toward the ultimate conservative scheme: following the quest
Journal of Computational Physics
High Order Fluctuation Schemes on Triangular Meshes
Journal of Scientific Computing
High-order accurate implementation of solid wall boundary conditions in curved geometries
Journal of Computational Physics
On uniformly high-order accurate residual distribution schemes for advection-diffusion
Journal of Computational and Applied Mathematics
Discontinuous fluctuation distribution
Journal of Computational Physics
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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 P"k elements, is globally continuous. A natural sub-triangulation of these elements allows to reuse the simple distribution schemes previously developed for linear P"1 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.