| Abstract: | In this article we present a new family of high order accurate ArbitraryLagrangian-Eulerian one-step WENO finite volume schemes for the solution of stiffhyperbolic balance laws. High order accuracy in space is obtained with a standardWENO reconstruction algorithm and high order in time is obtained using the localspace-time discontinuous Galerkin method recently proposed in [20]. In the Lagrangianframework considered here, the local space-time DG predictor is based on a weakformulation of the governing PDE on a moving space-time element. For the space-time basis and test functions we use Lagrange interpolation polynomials defined bytensor-product Gauss-Legendre quadrature points. The moving space-time elementsare mapped to a reference element using an isoparametric approach, i.e. the space-time mapping is defined by the same basis functions as the weak solution of the PDE.We show some computational examples in one space-dimension for non-stiff and forstiff balance laws, in particular for the Euler equations of compressible gas dynamics,for the resistive relativistic MHD equations, and for the relativistic radiation hydrodynamics equations. Numerical convergence results are presented for the stiff case up tosixth order of accuracy in space and time and for the non-stiff case up to eighth orderof accuracy in space and time. |
