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.
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