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

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 di...

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Bibliographic Details
Published in:Journal of scientific computing 2016-11, Vol.69 (2), p.866-891
Main Authors: Jaust, Alexander, Schütz, Jochen, Seal, David C.
Format: Article
Language:English
Subjects:
Accuracy
Algorithms
Computational Mathematics and Numerical Analysis
Conservation laws
Galerkin method
Integrators
Mathematical and Computational Engineering
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Methods
Ordinary differential equations
Partial differential equations
Solvers
Theoretical
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Summary: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.
ISSN:0885-7474
1573-7691
DOI:10.1007/s10915-016-0221-x