\n",
"\n",
"\n",
"### Defining transformation to collision space"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAoIAAAAVCAYAAADSDI/HAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAI60lEQVR4Ae2d7XHcNhCGaU0KUJQO5A6kuILIHUjuIFYHzk/pX0buwEkFHrsDJxVkog7kDuKog8v7ng4XEgcsPgiCgADM8EgCIHbxYJdckkdyuLm5eYfpYTedbTabwTSh/NSUX0JeCbqVoIM0FiXoV4IOnZHZvyUuqqyE8StBB8XDNC9BvxJ0MLFReSXoV4IOioc+L0G3EnTQuYzXS9CvBB3GTMbLLt1QPon7joZh+AHT9e3t7UtM91g+SMh/h8yzg4JyMk53Oq6iUQV8yKUzcltHZyQz6nxkPiztjDojNwG5RrchmQ9LOyOZkcgHMct7TC/RxGdMJy8QGd5h4Qsy/zC1i/xL5L/C/Be9HHnclukfTGz0DnlfmZEy+chBHQarj5j/llK2qy3IW52P0hG6MFj/hOkcy48qX82R1ywj9P0UHJQN/4jlb1xH/uTkp0RGHD/oJY4t68xNkOH055b5KL6usWiZEfpepZ/56q1sYM4csqrzs5x8FFvIFPd5KC/qeJaLka8cHz6os43/xEAQlY4xKH9ifq4GR82R9zeWf8WcEeWAOesy7zWWkwWDaMtbzq7uT5gfBEHUMXWCnBL4UIffMTGwYYBD5/nexqBRRjw4fUDfX2O+TVimA3BHQnudnASVwgh6BI3tU8/ifnd99vLnRvkEjUWjjGr1syC94zzsaatK/Swnn1r9LAsj2E+QHNd+COXbQPDIYdSs9EGvg43fIu8Y820QyHIsP2LG9YP6LI9JEXIomzrnSqvyYSfJHdMVpmusfvToeHOMwITjRD77BF68Okib5RVUPZXCKHRs9X54rYNFqD83xYcQwSh0LJpjBExV+lmE3jSJ4FSrn6GjoeMazEZtUKufZWQUOhZe+yFXIPgGA2O61XqFjk9uqe0G8i/ML7ANo/oUKUjOTlfqnEq+qw9r83Hpd1DeKKMLgHgw2AWvBPKEhmdZ+1QQo71OCy/U6mcLY4lvvkEbIqxa/SxI73irGGr1s1x8gtEW5Ge5GAXJ8eVjDQTRAP/7ZrvFS2V4K1JPqj7LU6QYOdThTQrhUhuF8JFUlMpaY8SA7yvGjFcATcl04lACI5OuS+TV6mdLsEjZZks2RG61+lmM3jF2Uquf5eITw5TblOBnuRjFyHHy+U4gz/9TUegk4WBqOmhO6mDlRM8IXZ8hhzpTd9OVzFA1pPqr8pEU8yhrihFsiWfipsT/Uw4oN13dXpWRSdkl8mr1syVYLNBmEzakuNXqZ5F6q257zWv2sxx8vCDaK63uZ7kYRcpx8rFeEQRzPnjwYGCvgjzb1RVu4hMsGpqeZMXKoc6TW32TVtOtrM1nTk+aZwSHYhBIO1FPEus812ak67PUeq1+thSPlO22YkNWZrX6mYfe1j5bCp6Vny3Ax4LNK7tIP8vFyEOOk48UCDKYM93+9RkZvpswRzLJoc45AsEa+NjGoDN6ekjkM5zovQVSDYwsqifPrtXPkoMIbLDbUL1+xofIpP1DoCl4Va/Jz9bgY4NYqp/lYuSS4+QjBYI8gzFd9WOjtqTOevhewbkpVg7vh6e4IunSf20+Lv2k8qYZIfjjk1T8z6DtljHZrc1IGr+UZbX6WUoGS7XVig0Z+dXqZ556G/ssZD4bP1uIj4DOWVScn+Vi5CnHyUcKBI30IVgFh6ZgS+VR8Kw0Q44tQJulj+/GM/T2FZGiXrOMMD58VcoJ5vt3ClqArsrIolPy7Bn22gSfmcCbZVSrnwXoHWQaz8XPluITBPOwclF+lotRgBwnHykQ5BmMCux09Pzzoen2KwUysTxFipFDnaWzrxR6sY0S+MT2pUlGcBw+Cc9PKe6vBGKZn+Ix2XIJjGLHN3S7Wv0stJ+567dkQ3u2tfpZoN77/gYsVO1nGfgEoJxULcbPcjEKlOPkIwWCvKpnOkByBHhPmg9L6OkcGfdQ8lEVYJlKxCZvOSMBDEadVyRn6kVxJfAZdTtosTlGGO8zEDJ9KpHBoenEoQRG3oM6055r9bNcfLzlaBVbsqFt15fws5m2rYZE2l8PvnrP1KVaP8vER41V6LwIP8vFyFfOCKKTjxQI3qOhV6PG9otQhK9m+YY5D6LbhGUGfHx/389POdvXcjDvX5TxM3HByVeO1vA2GNXyJqs7XaP12jW2Op9Jp55W1J+NOfBSaooRxpsnNNwJ8+XR/NTcfkLeNdb3Jy4jaKszGunCRevYQv8m/SwXH02OOBZa3WZsiP2GHSb3s7m2PRoPaX/tpfdcXbC913FzpDMXV7ch33Gdy0frN1et+zytbjOMfMcilI8UCH5EY2dag+NVwud3Wu8w8Zut/N4tv/NLh9smLPMAyzMxHoB5sIpJTjlao3xp5xctb7KaSK9S+AzozydO6CT//8a0XUeeWn/K/f+3NUa0B+7syUOfTEEgSRXByGdsUadZP8vIZ/CRRcMZpdZsKLmfJbJtDom0v/bSO5EuNR7PcvKp1c9yMfKSM9oHcdG5Hxpubm7uMF1sNptBn5D/gOlMzw9dRxuXmI5DtwutDxmnmB58t5urF2VhqoYPuUDfzshg62Ob6YwO9wWdj8xkzKf7mR+rED9D3dnHELRR1f46hM/O5mYxqo1P9zO3n7lsCOXb+E+6IshI8uADx8yMSPxvlu3KS0Rz1k34cmDq7Jvm6lUbH3LpjNzW0RnJjDofmQ9LO6O0jObuq6lNbfvrbkNpbYitzbWjZ2lDYiCI4I3/abA9VekeItRAG7wlnOK9gqI8yOGtP+rq9Wm5FHrtZFXBh/Cgb2ckWlFn5MDTbcgFqPuZB6EwP8N+K8kxBO3045kwOjXxYTegbz+eyePpzedIaEcV8VUbfAFvbHqLAbN9vSG2TdN21PHaVGDJS6VXLXyIoTOyGMMouzMawTAsdj4GKFpWZ6QBMayGMEq1r6YateyvQ/iwX6kY1cKHfe6MSMGevPm84D1itKOe/r1C0LZ/2EO1v4u8LzMFdEqs9xx68WEVfg7I+doY70YDKpbOh13pjNwD2hnJjDofmQ9LO6POyE1ArtFtSObD0s5IZuTisyvnhTO+YeTqP+82TfEYFbz0AAAAAElFTkSuQmCC",
"text/latex": [
"$\\displaystyle \\left[ \\left( 0, \\ 0\\right), \\ \\left( 0, \\ 1\\right), \\ \\left( 0, \\ 2\\right), \\ \\left( 1, \\ 0\\right), \\ \\left( 1, \\ 1\\right), \\ \\left( 1, \\ 2\\right), \\ \\left( 2, \\ 0\\right), \\ \\left( 2, \\ 1\\right), \\ \\left( 2, \\ 2\\right)\\right]$"
],
"text/plain": [
"[(0, 0), (0, 1), (0, 2), (1, 0), (1, 1), (1, 2), (2, 0), (2, 1), (2, 2)]"
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"from lbmpy.moments import moment_matrix, moments_up_to_component_order, exponents_to_polynomial_representations\n",
"moment_exponents = list(moments_up_to_component_order(2, 2))\n",
"moment_exponents"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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",
"text/latex": [
"$\\displaystyle \\left( 1, \\ y, \\ y^{2}, \\ x, \\ x y, \\ x y^{2}, \\ x^{2}, \\ x^{2} y, \\ x^{2} y^{2}\\right)$"
],
"text/plain": [
"⎛ 2 2 2 2 2 2⎞\n",
"⎝1, y, y , x, x⋅y, x⋅y , x , x ⋅y, x ⋅y ⎠"
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"moments = exponents_to_polynomial_representations(moment_exponents)\n",
"moments"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"| \n", " Moment-Based Method\n", " | \n", "Stencil: D2Q9 | \n", "Zero-Centered Storage: ✗ | \n", "Force Model: None | \n", "
|---|
| \n", " Continuous Hydrodynamic Maxwellian Equilibrium\n", " | \n", "\n", " $f (\\rho, \\left( u_{0}, \\ u_{1}\\right), \\left( v_{0}, \\ v_{1}\\right)) \n", " = \\frac{\\rho e^{\\frac{- \\left(- u_{0} + v_{0}\\right)^{2} - \\left(- u_{1} + v_{1}\\right)^{2}}{2 c_{s}^{2}}}}{2 \\pi c_{s}^{2}}$\n", " | \n", "|
|---|---|---|
| Compressible: ✓ | \n", "Deviation Only: ✗ | \n", "Order: 2 | \n", "
| Relaxation Info | ||
|---|---|---|
| Moment | \n", "Eq. Value | \n", "Relaxation Rate | \n", "
| $1$ | \n", "$\\rho$ | \n", "$\\omega$ | \n", "
| $y$ | \n", "$\\rho u_{1}$ | \n", "$\\omega$ | \n", "
| $y^{2}$ | \n", "$c_{s}^{2} \\rho + \\rho u_{1}^{2}$ | \n", "$\\omega$ | \n", "
| $x$ | \n", "$\\rho u_{0}$ | \n", "$\\omega$ | \n", "
| $x y$ | \n", "$\\rho u_{0} u_{1}$ | \n", "$\\omega$ | \n", "
| $x y^{2}$ | \n", "$c_{s}^{2} \\rho u_{0}$ | \n", "$\\omega$ | \n", "
| $x^{2}$ | \n", "$c_{s}^{2} \\rho + \\rho u_{0}^{2}$ | \n", "$\\omega$ | \n", "
| $x^{2} y$ | \n", "$c_{s}^{2} \\rho u_{1}$ | \n", "$\\omega$ | \n", "
| $x^{2} y^{2}$ | \n", "$c_{s}^{4} \\rho + c_{s}^{2} \\rho u_{0}^{2} + c_{s}^{2} \\rho u_{1}^{2}$ | \n", "$\\omega$ | \n", "
| $$vel0Term \\leftarrow f_{4} + f_{6} + f_{8}$$ |
| $$vel1Term \\leftarrow f_{1} + f_{5}$$ |
| $$\\rho \\leftarrow f_{0} + f_{2} + f_{3} + f_{7} + vel0Term + vel1Term$$ |
| $$u_{0} \\leftarrow \\frac{- f_{3} - f_{5} - f_{7} + vel0Term}{\\rho}$$ |
| $$u_{1} \\leftarrow \\frac{- f_{2} + f_{6} - f_{7} - f_{8} + vel1Term}{\\rho}$$ |
| $$\\delta_{\\rho} \\leftarrow \\rho - 1$$ |
| $$d_{0} \\leftarrow f_{0} + \\omega \\left(c_{s}^{4} \\rho + c_{s}^{2} \\rho u_{0}^{2} + c_{s}^{2} \\rho u_{1}^{2} - f_{5} - f_{6} - f_{7} - f_{8}\\right) - \\omega \\left(c_{s}^{2} \\rho - f_{1} - f_{2} - f_{5} - f_{6} - f_{7} - f_{8} + \\rho u_{1}^{2}\\right) - \\omega \\left(c_{s}^{2} \\rho - f_{3} - f_{4} - f_{5} - f_{6} - f_{7} - f_{8} + \\rho u_{0}^{2}\\right) + \\omega \\left(- f_{0} - f_{1} - f_{2} - f_{3} - f_{4} - f_{5} - f_{6} - f_{7} - f_{8} + \\rho\\right)$$ |
| $$d_{1} \\leftarrow f_{1} - \\frac{\\omega \\left(c_{s}^{2} \\rho u_{1} - f_{5} - f_{6} + f_{7} + f_{8}\\right)}{2} + \\frac{\\omega \\left(- f_{1} + f_{2} - f_{5} - f_{6} + f_{7} + f_{8} + \\rho u_{1}\\right)}{2} - \\frac{\\omega \\left(c_{s}^{4} \\rho + c_{s}^{2} \\rho u_{0}^{2} + c_{s}^{2} \\rho u_{1}^{2} - f_{5} - f_{6} - f_{7} - f_{8}\\right)}{2} + \\frac{\\omega \\left(c_{s}^{2} \\rho - f_{1} - f_{2} - f_{5} - f_{6} - f_{7} - f_{8} + \\rho u_{1}^{2}\\right)}{2}$$ |
| $$d_{2} \\leftarrow f_{2} + \\frac{\\omega \\left(c_{s}^{2} \\rho u_{1} - f_{5} - f_{6} + f_{7} + f_{8}\\right)}{2} - \\frac{\\omega \\left(- f_{1} + f_{2} - f_{5} - f_{6} + f_{7} + f_{8} + \\rho u_{1}\\right)}{2} - \\frac{\\omega \\left(c_{s}^{4} \\rho + c_{s}^{2} \\rho u_{0}^{2} + c_{s}^{2} \\rho u_{1}^{2} - f_{5} - f_{6} - f_{7} - f_{8}\\right)}{2} + \\frac{\\omega \\left(c_{s}^{2} \\rho - f_{1} - f_{2} - f_{5} - f_{6} - f_{7} - f_{8} + \\rho u_{1}^{2}\\right)}{2}$$ |
| $$d_{3} \\leftarrow f_{3} + \\frac{\\omega \\left(c_{s}^{2} \\rho u_{0} + f_{5} - f_{6} + f_{7} - f_{8}\\right)}{2} - \\frac{\\omega \\left(f_{3} - f_{4} + f_{5} - f_{6} + f_{7} - f_{8} + \\rho u_{0}\\right)}{2} - \\frac{\\omega \\left(c_{s}^{4} \\rho + c_{s}^{2} \\rho u_{0}^{2} + c_{s}^{2} \\rho u_{1}^{2} - f_{5} - f_{6} - f_{7} - f_{8}\\right)}{2} + \\frac{\\omega \\left(c_{s}^{2} \\rho - f_{3} - f_{4} - f_{5} - f_{6} - f_{7} - f_{8} + \\rho u_{0}^{2}\\right)}{2}$$ |
| $$d_{4} \\leftarrow f_{4} - \\frac{\\omega \\left(c_{s}^{2} \\rho u_{0} + f_{5} - f_{6} + f_{7} - f_{8}\\right)}{2} + \\frac{\\omega \\left(f_{3} - f_{4} + f_{5} - f_{6} + f_{7} - f_{8} + \\rho u_{0}\\right)}{2} - \\frac{\\omega \\left(c_{s}^{4} \\rho + c_{s}^{2} \\rho u_{0}^{2} + c_{s}^{2} \\rho u_{1}^{2} - f_{5} - f_{6} - f_{7} - f_{8}\\right)}{2} + \\frac{\\omega \\left(c_{s}^{2} \\rho - f_{3} - f_{4} - f_{5} - f_{6} - f_{7} - f_{8} + \\rho u_{0}^{2}\\right)}{2}$$ |
| $$d_{5} \\leftarrow f_{5} - \\frac{\\omega \\left(f_{5} - f_{6} - f_{7} + f_{8} + \\rho u_{0} u_{1}\\right)}{4} - \\frac{\\omega \\left(c_{s}^{2} \\rho u_{0} + f_{5} - f_{6} + f_{7} - f_{8}\\right)}{4} + \\frac{\\omega \\left(c_{s}^{2} \\rho u_{1} - f_{5} - f_{6} + f_{7} + f_{8}\\right)}{4} + \\frac{\\omega \\left(c_{s}^{4} \\rho + c_{s}^{2} \\rho u_{0}^{2} + c_{s}^{2} \\rho u_{1}^{2} - f_{5} - f_{6} - f_{7} - f_{8}\\right)}{4}$$ |
| $$d_{6} \\leftarrow f_{6} + \\frac{\\omega \\left(f_{5} - f_{6} - f_{7} + f_{8} + \\rho u_{0} u_{1}\\right)}{4} + \\frac{\\omega \\left(c_{s}^{2} \\rho u_{0} + f_{5} - f_{6} + f_{7} - f_{8}\\right)}{4} + \\frac{\\omega \\left(c_{s}^{2} \\rho u_{1} - f_{5} - f_{6} + f_{7} + f_{8}\\right)}{4} + \\frac{\\omega \\left(c_{s}^{4} \\rho + c_{s}^{2} \\rho u_{0}^{2} + c_{s}^{2} \\rho u_{1}^{2} - f_{5} - f_{6} - f_{7} - f_{8}\\right)}{4}$$ |
| $$d_{7} \\leftarrow f_{7} + \\frac{\\omega \\left(f_{5} - f_{6} - f_{7} + f_{8} + \\rho u_{0} u_{1}\\right)}{4} - \\frac{\\omega \\left(c_{s}^{2} \\rho u_{0} + f_{5} - f_{6} + f_{7} - f_{8}\\right)}{4} - \\frac{\\omega \\left(c_{s}^{2} \\rho u_{1} - f_{5} - f_{6} + f_{7} + f_{8}\\right)}{4} + \\frac{\\omega \\left(c_{s}^{4} \\rho + c_{s}^{2} \\rho u_{0}^{2} + c_{s}^{2} \\rho u_{1}^{2} - f_{5} - f_{6} - f_{7} - f_{8}\\right)}{4}$$ |
| $$d_{8} \\leftarrow f_{8} - \\frac{\\omega \\left(f_{5} - f_{6} - f_{7} + f_{8} + \\rho u_{0} u_{1}\\right)}{4} + \\frac{\\omega \\left(c_{s}^{2} \\rho u_{0} + f_{5} - f_{6} + f_{7} - f_{8}\\right)}{4} - \\frac{\\omega \\left(c_{s}^{2} \\rho u_{1} - f_{5} - f_{6} + f_{7} + f_{8}\\right)}{4} + \\frac{\\omega \\left(c_{s}^{4} \\rho + c_{s}^{2} \\rho u_{0}^{2} + c_{s}^{2} \\rho u_{1}^{2} - f_{5} - f_{6} - f_{7} - f_{8}\\right)}{4}$$ |
| Name | Runtime | Adds | Muls | Divs | Total |
|---|---|---|---|---|---|
| OriginalTerm | - | 245 | 248 | 2 | 495 |
| sympy_cse | 30.74 ms | 82 | 36 | 1 | 119 |