A clumpy fluid model of plasma dynamics

Summary form only given, as follows. The problem of using the Vlasov-Maxwell set of equations as a basis for numerical modeling of the dynamics of collisionless plasmas is a vexing one. The Vlasov equation itself is a seven dimensional object, which is numerically untenable. If one chooses to simplify the approach by integrating over the unobserved velocity components of the Vlasov equation coupled fluid equations emerge with no natural rules for closure. We present an alternative to the fluid method which avoids the closure problem, but at the cost of somewhat increased computational complexity. Rather than integrating over all of velocity space we perform separate integrations over small, contiguous subdomains of velocity space. In each subdomain the distribution function is simple enough that accurate integrations may be performed using Gaussian quadrature with a small number of points (N /spl les/ 7). The value of the distribution function at these N nodal points permits us to find the first N + 1 moments, and these are used to solve the fluid equations for N moments in each subdomain with boundary values provided by neighboring subdomains. After each time step the process is inverted, and the N moments are used to evaluate the distribution function at N nodal points which again allows the calculation of the N + 1/sup th/ moment, necessary to close the fluid equations, and the process is repeated. Several examples of the application of this method are offered.