Boundary variation diminished conservative semi-Lagrangian method for both compressible and incompressible flows

Abstract

1. Bo u n d a ry v a ri a tio n di mi ni s h e d c o n s e rv a tiv e s e mi-L a g r a n gi a n m e t h o d fo r b o t h c o m p r e s si bl e a n d inc o m p r e s si bl e flow s. P hy sic s of Fl ui d s 3 3 ,

Third-order less oscillatory and less diffusive compact stencil-based upwind schemes, and their applications to incompressible flows and free surface flows

“…We propose the CSLT (CSL with tangent hyperbolic function) scheme which uses a hyperbolic tangent function as the interpolation function. A similar scheme has been proposed in [16]. In [16], only cell averages were used to construct the hyperbolic tangent function (like standard finite volume methods) and a wider stencil (three cells) was used.…”

“…A similar scheme has been proposed in [16]. In [16], only cell averages were used to construct the hyperbolic tangent function (like standard finite volume methods) and a wider stencil (three cells) was used. In the proposed scheme, not only cell averages but also boundary values are used (like CIP-CSL schemes) and a shorter stencil (one cell average and two boundary values) is used.…”

“…where φ is the scalar and u is the velocity. The proposed method is based on the constrained interpolation profile-conservative semi-Lagrangian (CIP-CSL) schemes [27,36,34,18,35,15,16].…”