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In this paper we apply implicit two-derivative multistage time integrators to conservation laws in one and two dimensions. The one dimensional solver discretizes space with the classical discontinuous Galerkin method, and the two dimensional solver uses a hybridized discontinuous Galerkin spatial discretization for efficiency. We propose methods that permit us to construct implicit solvers using each of these spatial discretizations, wherein a chief difficulty is how to handle the higher derivatives in time. The end result is that the multiderivative time integrator allows us to obtain high-order accuracy in time while keeping the number of implicit stages at a minimum. We show numerical results validating and comparing methods.

Implicit Multistage Two-Derivative Discontinuous Galerkin Schemes for Viscous Conservation Laws