Regular ArticleOptimized Compact-Difference-Based Finite-Volume Schemes for Linear Wave Phenomena
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2024, Journal of Computational PhysicsNew hybrid compact schemes for structured irregular meshes using Birkhoff polynomial basis
2020, Journal of Computational PhysicsCitation Excerpt :Compact schemes have been extensively accustomed to the simulations of initial boundary value problems on various collocated and staggered meshes [1–6].
Hybrid sixth order spatial discretization scheme for non-uniform Cartesian grids
2017, Computers and FluidsCitation Excerpt :Despite performance gains by the use of non-uniform compact schemes, the present method is limited to geometries with grids which vary along mutually orthogonal directions only. Many Padé compact schemes were designed with implicit closures for the boundary and near-boundary points [1,10,17,32], and it was noted [26] that the resultant schemes displayed anti-diffusion near the inflow of the domain. In [17], performance of numerical first derivative at interior nodes was characterized by an equivalent wavenumber (keq), without addressing the issues of boundary closure schemes.
A scalable fully implicit method with adaptive time stepping for unsteady compressible inviscid flows
2016, Computers and StructuresCitation Excerpt :Compared to the general second order methods such as the LLF scheme, the main advantage of the compact schemes is their capability to achieve arbitrarily high order formal accuracy in smooth regions while maintaining stable, sharp discontinuity transitions, and non-oscillatory. Ref. [11] combines the compact schemes with finite volume formulation, which presents a class of arbitrary high order finite volume scheme. In [10,30,39], the ideas of high order accurate weighted essentially nonoscillatory (WENO) and upwind schemes are introduced into the compact schemes, which can obtain more accurate results and lead to substantial reduction in the total computing time.
A new alternating bi-diagonal compact scheme for non-uniform grids
2016, Journal of Computational PhysicsCitation Excerpt :Compact schemes for solving PDE originated from Padé schemes for discretization of ODEs and the former can be found in [1,8,11,12,25] among many other references. For example, optimized schemes have been used for time-domain Maxwell equation in [5]. A comprehensive account of compact schemes and GSA employed to test the numerical properties of space–time dependent problems can be found in [13].
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Corresponding author. OAI (ICOMP).