Eventos Anais de eventos
ENCIT 2022
19th Brazilian Congress of Thermal Sciences and Engineering
TRUNCATION ERROR EQUIVALENT BOUNDARY CLOSURE SCHEMES FOR HIGH-ORDER SPATIAL DISCRETIZATION
Submission Author:
João Pedro Marques Mendonça Lira , RJ
Co-Authors:
João Pedro Marques Mendonça Lira, Leonardo Santos de Brito Alves, Juan Carlos Assis da Silva
Presenter: Juan Carlos Assis da Silva
doi://10.26678/ABCM.ENCIT2022.CIT22-0202
Abstract
The time accurate simulations of initial value partial differential equations often require high-order spatial discretization schemes as well. The use of near boundary and boundary schemes with the same accuracy-order of the domain scheme, however, leads to numerical instability on uniform meshes. CFL numbers must, in turn, be reduced, which significantly increases CPU times. Two solutions are often employed to mitigate this issue: 1) mesh refinement at the boundaries and/or 2) lower order near boundary and boundary schemes. In the present paper, an alternative approach is proposed. Novel near boundary and boundary closure schemes are derived in such a way as to have the same first N terms of the domain scheme truncation error. Fourth and sixth-order schemes are tested on a classical convection-diffusion equation in order to verify the value of N required to prevent the CFL number reduction. At the present time, these schemes have been derived and the authors are implementing them on the test problem to evaluate their impact.
Keywords
Truncation Error, Spatial Discretization
