7/1/2023 0 Comments Gmsh define dirichletbc fenics![]() In the first several sections there will be a lot of math. So, I picked a problem that I in fact encountered in practice and would like to share how to solve it. Indeed, how you are going to use in practice a solution of a Poisson equation Δ□=6? This is the problem from which the FEniCS tutorial starts. There are a lot of tutorials how to use FEniCS, but most of them are not related to practice. The learning curve is still steep, but once you get it, it’s no brainer and is a lot of fun. This library solves PDE using the finite element method (FEM). It was so great that I decided to write a paper about my endeavor with calculating this project. I was so fascinated when I found a great tool that made the work very easy. For example, how much more dollars you will spend on heating if you make another window in the north wall of your house? Fortunately, nowadays we have in our possession a lot of tools that simplify hundredfold the task of solving PDE and help getting answers to practical questions that you can use even at your home, for DIY or just for fun. The complicity is regrettable, considering PDEs describe a plethora of phenomena around us that we encounter every second, whether we drink coffee or play a drum. Partial differential equations (PDE) is a complicated mathematical topic. Unfortunately, to solve the problem numerically one has to solve a partial differential equation. Therefore, maybe there is some optimal angle of the spiral?Īll these questions would be very time and material consuming to answer by experimenting with the real cylinders and spirals. What will be the capacitance? Will it change significantly with the water level? How it will change with the spiral angle? What is the best strategy: make narrow stripes and wind them tightly or make wide stripes and wind them with a moderate spiral? Indeed, one may think that if we tightly wind two narrow stripes, each loop will interact more with loops above and below than across the cylinder, thus making it insensitive to the water inside. Then I thought: if I wind the stripes around the cylinder in a spiral, I probably will increase the capacitance and probably the sensitivity? However, I didn’t have answers to a lot of pragmatic questions. When the level of water changes, it changes the electric capacitance between the stripes, which then can be measured. One of the ideas (not mine, the kudos are to Robert Bond) was to place two stripes of foil on the sides of a cylinder that holds water. I was contemplating on how to make a water level sensor for a DIY project. Ok, the real reason behind this section is to explain why I have written this article and maybe get you a little bit excited about what you are going to learn from it. But, well, it doesn’t occupy the whole section. A spiral capacitor is a cylinder with two stripes of metal foil spiraling on the opposite sides along the cylinder length. Don’t google “spiral capacitor”, I came up with this term to call what I have done for a DIY project. ![]()
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