2015
DOI: 10.1016/j.cam.2014.11.047
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Hermitian approximation of the spherical divergence on the Cubed-Sphere

Abstract: International audiencePrevious work [7] showed that the Cubed-Sphere grid offers a suitable discrete framework for extending Hermitian compact operators [6] to the spherical setup. In this paper we further investigate the design of high-order accurate approximations of spherical differential operators on the Cubed-Sphere with an emphasis on the spherical divergence of a tangent vector field. The basic principle of this approximation relies on evaluating pointwise Hermitian derivatives along a series of great c… Show more

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Cited by 4 publications
(6 citation statements)
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References 25 publications
(55 reference statements)
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“…In this section, the Hermitian Compact Scheme on the Cubed Sphere (HCCS) is summarized (Croisille 2013, 2015; Brachet 2018; Brachet and Croisille 2019). Consider the spherical SW equations: (SW)htfalse(t,boldxfalse)+normal∇normalT·{hfalse(t,boldxfalse)boldufalse(t,boldxfalse)}=0,boldutfalse(t,boldxfalse)+normal∇normalT()12false|boldufalse(t,boldxfalse)false|2+ghfalse(t,boldxfalse)1em+.15em{ffalse(boldxfalse)+ζfalse(t,boldxfalse)}boldnfalse(boldxfalse)prefix×boldufalse(t,boldxfalse)=0. …”
Section: The Hccs Solver: a Cubed‐sphere Approximation For The Spherimentioning
confidence: 99%
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“…In this section, the Hermitian Compact Scheme on the Cubed Sphere (HCCS) is summarized (Croisille 2013, 2015; Brachet 2018; Brachet and Croisille 2019). Consider the spherical SW equations: (SW)htfalse(t,boldxfalse)+normal∇normalT·{hfalse(t,boldxfalse)boldufalse(t,boldxfalse)}=0,boldutfalse(t,boldxfalse)+normal∇normalT()12false|boldufalse(t,boldxfalse)false|2+ghfalse(t,boldxfalse)1em+.15em{ffalse(boldxfalse)+ζfalse(t,boldxfalse)}boldnfalse(boldxfalse)prefix×boldufalse(t,boldxfalse)=0. …”
Section: The Hccs Solver: a Cubed‐sphere Approximation For The Spherimentioning
confidence: 99%
“…We have normal∇normalT,normalΔfrakturhfalse(bold-italicsi,jkfalse)normal∇normalThfalse(bold-italicsi,jkfalse),normal∇normalT,normalΔ·frakturufalse(bold-italicsi,jkfalse)normal∇normalT·boldufalse(bold-italicsi,jkfalse),normal∇normalT,normalΔprefix×frakturufalse(bold-italicsi,jkfalse)normal∇normalTprefix×boldufalse(bold-italicsi,jkfalse). Since () is a centred approximation, each approximate differential operator is centred as well. Details on the design and applications of the discrete operators () are reported in Croisille (2013) 2015 and Brachet and Croisille (2019). They are not repeated here.…”
Section: The Hccs Solver: a Cubed‐sphere Approximation For The Spherimentioning
confidence: 99%
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“…In this context, accurately evaluating averaged quantities over the sphere such as mass, momentum, energy or total vorticity is particularly important. This is in particular the case for the finite difference scheme introduced in [4,5]. This scheme uses discrete unknowns located at the nodes of the Cubed Sphere.…”
Section: Introductionmentioning
confidence: 99%