| Abstract: | In this article we present a new family of high order accurate Arbitrary
Lagrangian-Eulerian one-step WENO finite volume schemes for the solution of stiff
hyperbolic balance laws. High order accuracy in space is obtained with a standard
WENO reconstruction algorithm and high order in time is obtained using the local
space-time discontinuous Galerkin method recently proposed in 20]. In the Lagrangian
framework considered here, the local space-time DG predictor is based on a weak
formulation of the governing PDE on a moving space-time element. For the space-time basis and test functions we use Lagrange interpolation polynomials defined by
tensor-product Gauss-Legendre quadrature points. The moving space-time elements
are 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 for
stiff 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 to
sixth order of accuracy in space and time and for the non-stiff case up to eighth order
of accuracy in space and time. |
