Why choosing implicit method in VoF eulerian model is the best option ?

 Imagine you're a detective trying to track down a mischievous gas bubble hiding in a swirling liquid. In the world of computational fluid dynamics (CFD), that bubble is your friend, and you're the CFD model trying to predict its movement.

There are two main ways to approach this case: explicit and implicit methods.

The Explicit Method: A Bit Too Eager

The explicit method acts like a rookie detective, bursting into every room at once. It constantly checks on the bubble's location and uses the information to predict its next move. This can be fast, but also prone to mistakes if the bubble's a sneaky one, zipping around too quickly.

The Implicit Method: The Mastermind

The implicit method, on the other hand, is a seasoned investigator. Instead of constantly chasing the bubble, it gathers all the clues (pressure, velocity, etc.) beforehand and solves a complex puzzle to predict where the bubble will be. This takes slightly longer, but the results are much more reliable, especially for those slippery gas bubbles.

Here's why the implicit method shines in VoF (Volume of Fluid) Eulerian models:

1. Sharper Interface: The implicit method treats the bubble's fuzzy edges with finesse. It doesn't let the liquid and gas mix and mingle more than they should, resulting in a crisper, more accurate representation of the interface.
2. Stability Under Pressure: When things get intense (high pressure differences), the explicit method can struggle. The implicit method, however, stays calm and collected, preventing the bubble from exploding or disappearing into thin air due to numerical errors.
3. Catching Up with Speedy Bubbles: Fast-moving bubbles can outrun the explicit method's grasp. The implicit method, with its clever calculations, can keep up with even the most agile gas bubbles.

So, while the explicit method might seem quicker on its feet, the implicit method proves to be the smarter, more reliable choice for VoF Eulerian models, especially when dealing with those tricky gas bubbles. It's the Sherlock Holmes of CFD, solving the case with precision and finesse.

Is reaching convergence in implicit method is much easier ?

You're absolutely right! Reaching convergence (finding a stable solution) is generally easier with implicit methods compared to explicit methods in VoF Eulerian models. Here's why:

• No Time Step Restriction: Explicit methods have a critical time step limitation. If you choose a time step that's too large, the calculations become unstable, and the bubble can go haywire in your simulation. The implicit method, however, doesn't have this constraint. It can take larger time steps without sacrificing stability, which means it reaches convergence faster.
• Smoother Sailing: Remember how the explicit method constantly chases the bubble? This can lead to oscillations in the solution, making it jumpy and inaccurate. The implicit method, by considering all the forces at play beforehand, avoids these oscillations, leading to a smoother, more direct path to convergence.

However, there's a catch:

• Computational Cost: The implicit method's complex calculations come at a price. It requires solving a system of equations, which can be computationally expensive, especially for complex simulations.

So, while easier convergence is a big advantage of implicit methods, it's important to consider the computational cost in relation to the complexity of your simulation. For simpler problems, the explicit method might be a good trade-off between speed and accuracy.

Ultimately, the choice between explicit and implicit methods depends on the specific needs of your VoF Eulerian model. If high accuracy and convergence are paramount, and computational resources are available, the implicit method reigns supreme. But if speed is a bigger concern for a less complex simulation, the explicit method might be a viable option.