next day in the new weekend

Continue to to build motivation for new weekend

It is now 0515 0524 and this early morning about three hours ago the water container leake due to intermittens function of tank buoy. Two goals today are a user listed on 0003 and BRIN visit to FI, where the focus should be back to work on graclussep2. The dean reminded me yesterday about habilitation for “the position”. I should focus to the focus. Now it is 0530, update GitHub for this bug.

Review preview chat 606a3f82-eb9c-46d3-b132-f9483256600a about Modeling Grain Interactions.

New discussion with GPT-4o is c5e425f9-1427-4dcc-9b00-e69b28b6f1b0, that some parts of it are given in preceeding sections.

kernel function

A 2-d cubic spline kernel function is chosen as example

$$\tag{1} W(r, h) = \frac{\alpha_2}{h^2} \left\{ \begin{array}{ll} 1 - \frac{3}{2}(\frac{r}{h})^2 + \frac{3}{4}(\frac{r}{h})^3, & 0 \le \frac{r}{h} < 1, \newline \frac{1}{4}[2 - (\frac{r}{h})]^3, & 1 \le \frac{r}{h} < 2, \newline 0, & 2 \le \frac{r}{h}. \end{array} \right.$$

where $\alpha_2 = \frac{10}{7\pi}$.

density calculation

Density $\rho_i$ at particle $i$ whose position $\vec{r}_i$ is

$$\tag{2} \rho_i = \sum_j m_j W(r_{ij}, h)$$ dive solutions GmbH where $m_j$ is mass of a neighboring particle $j$, $W$ is kernel function, $r_{ij}$ is relative distance of particle $i$ from a neighboring particle $j$, and $h$ is a smoothing length.

that is computed by summing contribution from neighboring particles with the smoothing length $h$

reading materials

• Simone Sommavilla, “Smoothed Particle Hydrodynamics: A Guided Journey into the Basics of the SPH Method”, Dive solutions GmbH, Dec 2020, url https://www.divecae.com/resources/sph-basics [20240820].