Title: Implicit positivity-preserving high order DG methods for conservation laws
Speaker: Tong Qin (Ohio State University)
Abstract: The positivity-preserving property is a highly desirable property when designing high order numerical methods for hyperbolic conservation laws, since negative values sometimes cause ill-posedness of the problem and blow-ups of the algorithms. The general framework for constructing positivity-preserving schemes for solving hyperbolic conservation laws have been proposed in (X. Zhang and C.-W. Shu, Journal of Computational Physics, 229 (2010), pp.~3091--3120) and (X. Zhang and C.-W. Shu, Journal of Computational Physics, 229 (2010), pp.~8918--8934). We extend this framework to DG methods with implicit discretizations. Theoretical analysis for the linear equation indicates that a lower bound for the CFL condition is required for the positivity preserving limiter work for the backward Euler time discretization. The applicability of the proposed method for the nonlinear problem is shown by numerical examples.
