Lines Matching refs:x

12 \rho &= \rho_\infty\left(1+A\exp\left(\frac{-(\bar{x}^2 + \bar{y}^2)}{2\sigma^2}\right)\right) \\
14 E &= \frac{p_\infty}{\gamma -1}\left(1+A\exp\left(\frac{-(\bar{x}^2 + \bar{y}^2)}{2\sigma^2}\right)…
18 …e amplitude and width of the perturbation, respectively, and $(\bar{x}, \bar{y}) = (x-x_e, y-y_e)$…
21 The boundary conditions are freestream in the x and y directions. When using an HLL (Harten, Lax, v…
63 A cylinder with diameter $D=1$ is centered at $(0,0)$ in a computational domain $-4.5 \leq x \leq 1…
119 …is defined in terms of the Exner pressure, $\pi(\bm{x},t)$, and potential temperature, $\theta(\bm…
122 …rac{P_0}{( c_p - c_v)\theta(\bm{x},t)} \pi(\bm{x},t)^{\frac{c_v}{ c_p - c_v}} \, , \\ e &= c_v \th…
246 Algorithmically, a base node distribution is defined at the inlet (assumed to be $\min(x)$) and the…
253 The node locations used exactly at the inlet (assumed to be $\min(x)$) and linearly stretched/squee…
385 u &= V'_x + V \sin(\hat x) \cos(\hat y) \sin(\hat z) \\
386 v &= V'_y - V \cos(\hat x) \sin(\hat y) \sin(\hat z) \\
388 p &= p_0 + \frac{\rho_0 V_0^2}{16} \left ( \cos(2 \hat x) + \cos(2 \hat y)\right) \left( \cos(2 \ha…
393 where $\hat x = 2 \pi x / L$ for $L$ the length of the domain in that specific direction, $V$ is th…
394 The coordinate modification is done to transform a given grid onto a domain of $x,y,z \in [0, 2\pi)…
432 …elta u_2) &= \frac{\epsilon}{2 \pi} \, e^{0.5(1-r^2)} \, (-\bar{y}, \, \bar{x}) \, , \\ \delta T &…
435 where $(\bar{x}, \, \bar{y}) = (x-x_c, \, y-y_c)$, $(x_c, \, y_c)$ represents the center of the dom…
578 …er is whether the radius is applied in all 3 dimensions (sphere) or just in the x and y directions.