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We propose a novel deterministic particle method to numerically approximatethe Landau equation for plasmas. Based on a new variational formulation interms of gradient flows of the Landau equation, we regularize the collisionoperator to make sense of the particle solutions. These particle solutionssolve a large coupled ODE system that retains all the important properties ofthe Landau operator, namely the conservation of mass, momentum and energy, andthe decay of entropy. We illustrate our new method by showing its performancein several test cases including the physically relevant case of the Coulombinteraction. The comparison to the exact solution and the spectral method isstrikingly good maintaining 2nd order accuracy. Moreover, an efficientimplementation of the method via the treecode is explored. This gives a proofof concept for the practical use of our method when coupled with the classicalPIC method for the Vlasov equation.

A particle method for the homogeneous Landau equation