A Posteriori Stabilized Sixth-Order Finite Volume Scheme with Adaptive Stencil Construction: Basics for the 1D Steady-State Hyperbolic Equations

We propose an adaptive stencil construction for high-order accurate finite volume schemes a posteriori stabilized devoted to solve one-dimensional steady-state hyperbolic equations. High accuracy (up the sixth-order presently) is achieved, thanks polynomial reconstructions while stability provided with MOOD method which controls cell degree eliminating non-physical oscillations in vicinity of discontinuities. supplemented this scheme allowing reduce even further numerical dissipation. The shifted away from troubles (shocks, discontinuities, etc.) leading less oscillating reconstructions. Experimented on linear, Bürgers’, and Euler equations, we demonstrate that technique manages retrieve smooth solutions optimal order but also irregular ones without spurious oscillations. Moreover, numerically show approach allows dissipation still maintaining essentially non-oscillatory behavior.