2016 **Abstract:** A unified approach for the numerical solution of the 3D hyperbolic Euler equations using high order methods, namely continuous Galerkin (CG) and discontinuous Galerkin (DG) methods, is presented. First, we examine how classical CG that uses a global storage scheme can be constructed within the DG framework using constraint imposition techniques commonly used in the finite element literature. Then, we implement and test a simplified version in the Non-hydrostatic Unified Model of the Atmosphere (NUMA) for the c…

Help me understand this report

Search citation statements

Paper Sections

Select...

1

1

1

1

Citation Types

1

22

0

Year Published

2017

2022

Publication Types

Select...

6

1

Relationship

1

6

Authors

Journals

(23 citation statements)

1

22

0

“…A spherical perturbation of radius r 0 = 250 m, located at $\left({x}_{0},\phantom{\rule{0ex}{0ex}}{y}_{0},\phantom{\rule{0ex}{0ex}}{z}_{0}\right)=\left(0,0,350\right)\phantom{\rule{0ex}{0ex}}\mathrm{normalm}$ is added to the background state. The perturbation is defined by $${\theta}^{\prime}=\left(\begin{array}{cc}arrayarrayA\left[1+\mathrm{cos}\left(\frac{\pi r}{{r}_{0}}\right)\right]\phantom{\rule{1em}{0ex}}& arrayr\le {r}_{0},\\ array0\phantom{\rule{1em}{0ex}}& arrayr>{r}_{0},\end{array}\right)$$ with $r=\sqrt{\left({\left(x-{x}_{0}\right)}^{2}+{\left(y-{y}_{0}\right)}^{2}+{\left(z-{z}_{0}\right)}^{2}\right)}$ and A = 0.25 K as in Abdi and Giraldo (). Snapshots of the bubble at t = 0, 200 and 400 s are shown in Figure and a one‐dimensional cross‐section at x = y = 0 in Figure .…”

confidence: 99%

“…A spherical perturbation of radius r 0 = 250 m, located at $\left({x}_{0},\phantom{\rule{0ex}{0ex}}{y}_{0},\phantom{\rule{0ex}{0ex}}{z}_{0}\right)=\left(0,0,350\right)\phantom{\rule{0ex}{0ex}}\mathrm{normalm}$ is added to the background state. The perturbation is defined by $${\theta}^{\prime}=\left(\begin{array}{cc}arrayarrayA\left[1+\mathrm{cos}\left(\frac{\pi r}{{r}_{0}}\right)\right]\phantom{\rule{1em}{0ex}}& arrayr\le {r}_{0},\\ array0\phantom{\rule{1em}{0ex}}& arrayr>{r}_{0},\end{array}\right)$$ with $r=\sqrt{\left({\left(x-{x}_{0}\right)}^{2}+{\left(y-{y}_{0}\right)}^{2}+{\left(z-{z}_{0}\right)}^{2}\right)}$ and A = 0.25 K as in Abdi and Giraldo (). Snapshots of the bubble at t = 0, 200 and 400 s are shown in Figure and a one‐dimensional cross‐section at x = y = 0 in Figure .…”

confidence: 99%

“…and A = 0.25 K as in Abdi and Giraldo (2016). Snapshots of the bubble at t = 0, 200 and 400 s are shown in Figure 8 and a one-dimensional cross-section at x = y = 0 in Figure 9.…”

confidence: 99%

“…In many CFD applications, the finite-volume method is applied on a unstaggered grid using an approximate Riemann solver to calculate the volume interface fluxes. Therefore, despite performance difficulties, in recent years, many efforts have been made to implement the unstaggered Riemann solver for atmospheric applications (Abdi & Giraldo, 2016;Giraldo & Restelli, 2008;Katta et al, 2014;Kelly & Giraldo, 2012;Kopera & Giraldo, 2014;Ullrich et al, 2010;Ullrich & Jablonowski, 2012;Yang et al, 2010). However, compared to geophysical dynamical cores, the mathematical formulation of these solvers are complicated and computationally expensive.…”

confidence: 99%

“…This new version of NUMA is capable of handling two data layouts for CG and one for DG -similar to the unified construction of numa2dCGDG_AMR, the 2D adaptive mesh refinement version of NUMA. This unification in the 3D code unifies all NUMA codes into a single code-base which will greatly simplify the further improvement of the model (for more details about the unified NUMA code see Abdi and Giraldo [3]).…”

confidence: 99%

“…After year 2, the first stage of unification of the CG and DG codes was completed [3]. This resulted in a single code base that can solve the Euler equations using either CG or DG.…”

confidence: 99%