A Frequency Accurate Finite Difference Scheme for Burgers Equation
Physics and Astronomy
A method is presented for designing a one-step, explicit finite difference scheme for solving the inviscid Burgers equation based on an a priori specification of dissipation and phase accuracy requirements. Frequency accurate temporal and spatial approximations with undetermined coefficients are used, together with a set of constraints that ensure that the approximations converge as the spatial and temporal grid sizes approach zero and satisfy the Lax Equivalence Theorem. A practical design of the difference scheme using a heuristic zero placement method, combined with a stability requirement, results in a linear matrix problem which is solved to obtain the undetermined coefficients. The partial differential equation itself provides the relationship between the temporal and spatial frequency dependence in the numerical approximation.
Journal of Computational Acoustics
Orlin, P. A.,
Perkins, A. L.
(1998). A Frequency Accurate Finite Difference Scheme for Burgers Equation. Journal of Computational Acoustics, 6(3), 321-335.
Available at: https://aquila.usm.edu/fac_pubs/5144