Regular ArticleA Multidimensional Flux Function with Applications to the Euler and Navier-Stokes Equations
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A study of higher-order reconstruction methods for genuinely two-dimensional Riemann solver
2021, Journal of Computational PhysicsCitation Excerpt :Early successes emerged with the work of Collela [12], LeVeque [13] by building some level of multidimensionality out of the one-dimensional Riemann solvers. More attempts include the introductions of the multidimensionality into the one-dimensional Riemann solvers by Roe and Rumsey [14,15], the multidimensional HLLE scheme proposed by Wendroff [16], and the multidimensional extensions of Roe's linearized Riemann solvers by Abgrall [17,18], Fey [19,20], and Brio [21]. However, these schemes have been restricted for application because of their complex forms and high computational cost [22].
Improvement of the genuinely multidimensional ME-AUSMPW scheme for subsonic flows
2021, Computers and Mathematics with ApplicationsCitation Excerpt :In order to dispel such problem, many researchers conduct studies on the genuinely multidimensional Riemann solver. For example, Roe and Rumsey reconstructed the Roe scheme from one dimensional problem to multidimensional problem [16,17]. LeVeque proposed the multidimensional wave propagation scheme and Collela developed the corner transport upwind scheme [18,19].
A new genuinely two-dimensional Riemann solver for multidimensional Euler and Navier–Stokes Equations
2019, Computer Physics CommunicationsCitation Excerpt :By considering not only the information propagating normal to the cell interfaces, but also those propagating transverse to the cell interfaces, the multidimensional Riemann solvers are capable of capturing multidimensional complex flows accurately in theory. Following this idea, Roe and Rumsey introduced the multidimensionality into the one-dimensional Riemann solvers [23,24]. Collela proposed the corner transport upwind scheme [25] and LeVeque developed the multidimensional wave propagation scheme [26].
A genuinely two-dimensional Riemann solver for compressible flows in curvilinear coordinates
2019, Journal of Computational PhysicsA two-dimensional Riemann solver with self-similar sub-structure - Alternative formulation based on least squares projection
2016, Journal of Computational Physics