Abstract:In this article, we introduce and analyze the class of numerical schemes known as residual distribution or fluctuation splitting schemes. The root of this family of discretizations is found mainly in works aiming at generalizing the finite volume techniques to a genuinely multidimensional upwinding context, as in, for example (Hall, Morton, Ni, Roe). However, the final result is a numerical method sharing a lot with other techniques, such as finite element schemes (Carette, Deconinck, Paillere and Roe, 1995).
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“…where i are the degrees of freedom (DoFs). In this work, we consider a linear basis function (so the DoFs coincide with the mesh nodes), which satisfies [29]…”
Section: Steps To Define An Rd Discretizationmentioning
confidence: 99%
“…1). Now, we briefly recall the main steps required to obtain the spatial RD discretization of (1) (for the details see, e.g., [37,30,29]).…”
Section: Steps To Define An Rd Discretizationmentioning
confidence: 99%
“…Accordingly, F ij is the numerical finite volume evaluation of the flux f (w ) exchanged across ∂C ij and η ij = ∂Cij nij d is the integrated normal, where nij points outward C i . Between the integrated normal η ij (defined in the FV context) and the nodal normal vector η i introduced in (2) (in the RD context), the following geometrical relation holds within the triangle K [29]:…”
Section: From the Ale Fv To The Rd Discretizationmentioning
confidence: 99%
“…Residual distribution (or fluctuation splitting) schemes [27] are based on a continuous nodal finite element approximation of the solution and offer the possibility to achieve arbitrarily high order of accuracy on unstructured grids in a pretty simple way [28,29]. This type of spatial discretization relies on a compact stencil, an important feature that simplifies the derivation and implementation of the series of fictitious deformations used to describe connectivity changes.…”
“…where i are the degrees of freedom (DoFs). In this work, we consider a linear basis function (so the DoFs coincide with the mesh nodes), which satisfies [29]…”
Section: Steps To Define An Rd Discretizationmentioning
confidence: 99%
“…1). Now, we briefly recall the main steps required to obtain the spatial RD discretization of (1) (for the details see, e.g., [37,30,29]).…”
Section: Steps To Define An Rd Discretizationmentioning
confidence: 99%
“…Accordingly, F ij is the numerical finite volume evaluation of the flux f (w ) exchanged across ∂C ij and η ij = ∂Cij nij d is the integrated normal, where nij points outward C i . Between the integrated normal η ij (defined in the FV context) and the nodal normal vector η i introduced in (2) (in the RD context), the following geometrical relation holds within the triangle K [29]:…”
Section: From the Ale Fv To The Rd Discretizationmentioning
confidence: 99%
“…Residual distribution (or fluctuation splitting) schemes [27] are based on a continuous nodal finite element approximation of the solution and offer the possibility to achieve arbitrarily high order of accuracy on unstructured grids in a pretty simple way [28,29]. This type of spatial discretization relies on a compact stencil, an important feature that simplifies the derivation and implementation of the series of fictitious deformations used to describe connectivity changes.…”
In this paper, the author recounts his forty-year plus struggle to find a sound basis for understanding the computational fluid dynamics of compressible flow.
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