Simulating Transients from Already-Charged Capacitors?

[biergaizi]

Here's a brainteaser for all experts: What would be a good strategy for simulating transients from an already-charged capacitor, similar to setting an initial condition in circuit simulators? This way, perhaps one can realistically recreate many historical experiments of E&M, and it would be educational and insightful. Of course, we normally use openEMS for parameter extractions, so these kinds of simulations rarely have practical uses, and is a curiosity at best, so I call it a brainteaser.

Idea 1: Flat Port and Hard Excitation?

My solution: For simple parallel-plate capacitors, I guess it's probably doable by defining a lumped port as large as the metal plates, and by setting the excitation signal as a short hard pulse. During the first timestep, the lumped port adds a field directly to the simulation box as its initial condition, then the port is turned off, allowing the simulation to free-run in later timesteps.

Idea 2: Use the Field of One Simulation As the Initial Condition of the Next?

However hard-excitation method is only an approximation. To really define a charge capacitor as the initial condition, it requires prior knowledge of the entire electric field around the capacitor, including fringe fields, which in itself requires E&M simulation, especially for capacitors with irregular shapes.

So perhaps the only complete way is running a bootstrap simulation with a removed or disconnected load to charge the capacitor to its steady-state, perhaps by using a sufficiently long excitation and stopping the simulation in the middle. Then the electric field of the simulation box is exported. Finally the next simulation is restarted with the load connected using the previous electric field as the initial condition.

However, this method still has two problems:

1. Is forcefully loading a field even supported by openEMS/CSXCAD's standard API without hacking the code?
2. The process of connecting/removing load itself also distorts the electric field, as materials are added and removed during both simulations, so the physical change in the box must be minimized.

Your Idea?

I wonder if anyone has better ideas in similar simulations, especially if one wants to generalize it to capacitors of arbitrary materials and shapes. I know for sure that openEMS is not really designed for time-variant objects - supporting it in general would be a multi-physics problem far beyond the scope of openEMS. But as a brain-teaser, I wonder if anyone has better ideas.

[gadiLhv]

Hey @biergaizi

I think introducing initial conditions into the software is a wonderful idea. I wonder if the other commercial software have this feature. I'll check soon enough.

Let's look at the ideas you presented:

Idea 1: Flat Port and Hard Excitation?

In a sense, this is all that it takes. You set up the initial condition along the mesh, applying voltages to the mesh nodes, such that an integration will obtain the voltage you required.
However, the issue is that this is a distributed system. The wires connected to the discrete component are also affected by the impressed voltage.
What I don't know, that's supported, is a very short excitation. You need to set it up such that it will only last for the first time step. Even that is not a 100% correct, but it is rather close. The physical meaning of this, is that you magically opened a switch next to the capacitor, unleashing it's stored charges unto the world. If that suits you, fine.

Idea 2: Use the Field of One Simulation As the Initial Condition of the Next?

This is, naturally, the optimal solution, albeit computationally expensive. You can solve this by setting to excitations that start in two separate times. One after a long wait period, one after release.

If you are only interested in the discharge behavior, you can only set a long DC voltage excitation

However, this method still has two problems:

1. Is forcefully loading a field even supported by openEMS/CSXCAD's standard API without hacking the code?

It may be possible. If you look at the excitation setup in the C++ code, you can see that a custom excitation is available. I'd dig into that.

	case Excitation::GaissianPulse:
		m_Excite_Elem->QueryDoubleAttribute("f0",&f0);
		m_Excite_Elem->QueryDoubleAttribute("fc",&fc);
		exc->SetupGaussianPulse(f0, fc);
		break;
	case Excitation::Sinusoidal:  // sinusoidal excite
		m_Excite_Elem->QueryDoubleAttribute("f0",&f0);
		exc->SetupSinusoidal(f0);
		break;
	case Excitation::DiracPulse:
		FDTD_Opts->QueryDoubleAttribute("f_max",&f_max);
		exc->SetupDiracPulse(f_max);
		break;
	case Excitation::Step:
		FDTD_Opts->QueryDoubleAttribute("f_max",&f_max);
		exc->SetupStepExcite(f_max);
		break;
	case Excitation::CustomExcite:
		m_Excite_Elem->QueryDoubleAttribute("f0",&f0);
		FDTD_Opts->QueryDoubleAttribute("f_max",&f_max);
		exc->SetupCustomExcite(m_Excite_Elem->Attribute("Function"), f0, f_max);
		break;
	}

I have no idea if changing the core code is necessary, at this moment.

2. The process of connecting/removing load itself also distorts the electric field, as materials are added and removed during both simulations, so the physical change in the box must be minimized.

I discussed this earlier. It's not so much as "distorts", as much as understanding the physical meaning of it...

Your Idea?

If I had to choose an idea, it would be interacting with an external circuit solver that has transient abilities. It is a nightmare, but it is the most generic solution. The time-step parameters can be pushed back and forth, creating the dream that we call a "true transient simulation".

[biergaizi]

Is forcefully loading a field even supported by openEMS/CSXCAD's standard API without hacking the code?

It may be possible. If you look at the excitation setup in the C++ code, you can see that a custom excitation is available. I'd dig into that.

I know the excitation signal can be customized, but it's primarily designed to inject a "lumped" signal at a small port, as defined by an algebraic expression. In my purposed solution of reusing fields across simulations, the fields across a potentially very large region of the simulation domain (e.g. the 3D space around a large, charged capacitor as the initial condition) has to be exported and reloaded, up to the entire simulation box, so as far as I can see openEMS currently is not designed to do this.

Although it shouldn't be too difficult - it's just the same HDF5 export code, but in reverse... Hmmm, if we're going to implement this, it can be part of the a "checkpointing" feature as well - which is a useful feature in its own. Sounds like a useful feature to put on my personal TODO list.

[gadiLhv]

Hello again

I know the excitation signal can be customized, but it's primarily designed to inject a "lumped" signal at a small port, as defined by an algebraic expression. In my purposed solution of reusing fields across simulations, the fields across a potentially very large region of the simulation domain (e.g. the 3D space around a large, charged capacitor as the initial condition) has to be exported and reloaded, up to the entire simulation box, so as far as I can see openEMS currently is not designed to do this.

You can extend the lumped port excitation to a volume, but that is as far as it goes. A more generic solution will require what you suggeted.

Keep us up to date! Also, there are certain souls here anxious to here about your computational engine changes :)