Noise reduction of stochastic particle methods

Particle-based kinetic simulations have one major drawback: the statistical noise caused by the stochastic processes. If the velocity or temperature differences in the flow are small, this noise can be similar in magnitude to the actual physical values, rendering the simulation results worthless. In re-entry simulations, where the flow velocity and temperature are quite high, this is usually not a major problem, but in applications such as gas sensors or other microelectromechanical systems, the microscopic scales still cause important non-equilibrium effects while the velocities remain low. To reduce the statistical noise without increasing the number of simulation particles and thus the computational costs too much, new methods need to be developed.

Another type of kinetic methods that can be used to simulate rarefied gases are the Discrete Velocity Methods (DVM), which use a fully deterministic approach without random numbers that would generate statistical noise. These methods consist of a full discretization of the BGK equation using a grid in space, but also in velocity space, instead of simulation particles. An accurate second-order DVM without physical constraints on the temporal discretization has been developed and implemented in PICLas. This method is particularly efficient for 2D flows where the third dimension of space and velocity does not need to be considered. For low velocity flows, it leads to much more accurate results in much less time than its particle-based counterpart.

However, the fine discretization of particle velocities to use DVM for hypersonic flows with strong non-equilibrium effects remains a challenge. Coupling DVM with the particle solver of PICLas to create a multiscale solver where both methods can be used simultaneously to compensate for each other's weaknesses would therefore be beneficial. The development of particle simulation methods for noise reduction, possibly by combining DVM with stochastic particles, is therefore still ongoing.