Development of a Lagrange–Monte Carlo scheme for fluid modelling of SOL/divertor plasmas

Aiming at reproducing plasma detachment states with a three‐dimensional fluid code, we are developing the Lagrange–Monte Carlo (LG‐MC) scheme. It integrates two schemes, namely a Lagrange scheme for the convective part and a Monte Carlo scheme for the diffusive part. One advantage of the scheme is the semi‐implicit treatment of the pressure gradient term in the convective part, which is essential to solve pure convective problems. As a first step, several one‐dimensional (1D) test calculations have been carried out so far. In this paper, results of the two preliminary tests are presented: (a) a test for the Lagrange scheme solving convective equations, and (b) a test for the integrated LG‐MC scheme solving a convection–conduction equation. These tests confirm the conservative property of the Lagrange scheme and the reliability of the integrated LG‐MC scheme.