By edited by H. Usui and Y. Omura.
This can be a number of prolonged lecture notes of the tutorials given on the overseas college for house Simulations (ISSS)-7, March 2005, by means of the invited teachers who've been actively concerned with machine simulation options in area plasma physics.
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Additional info for Advanced methods for space simulations
The first term in expression (25) provides a first order 1 2,j upwind scheme. The middle term provides second order accuracy correction. The third is a transverse propagation term from the diagonally located subdomain. As it is well known, second order schemes can cause un-physical oscillations which may lead to negative values of the distribution function or even to numerical x instabilities. To avoid such instabilities we limit the physical flux Hi+ in the mid1 2,j dle, the second (order) term of Eq.
The middle term provides second order accuracy correction. The third is a transverse propagation term from the diagonally located subdomain. As it is well known, second order schemes can cause un-physical oscillations which may lead to negative values of the distribution function or even to numerical x instabilities. To avoid such instabilities we limit the physical flux Hi+ in the mid1 2,j dle, the second (order) term of Eq. (25). The limiter function, that applies directly to the derivatives, is given by x C R L Hi+1/2, j = Limiter Q i, j , Q i, j , Q i, j (26) where Limiter is a nonlinear function based on the gradient of the solution.
The open outflow boundaries + are indicated by flow arrows. Vx simulation domain fe V>0 x α outflow 0 V(x=0)<0 x f(x); x α fi V<0 x fe inflow fi Vd outflow inflow V(x=Lx)>0 x Lx Fig. 4. Schematics of boundary conditions f e (solid line) depicts an electron—and f i (dotted line) an ion distribution function at the two inflow boundaries − . The outflow boundaries + are kept open, indicated by flow arrows, as implemented by B¨uchner and Elkina (2006b). 5 Vlasov Code Applications in Space Physics A common space physics application of Vlasov-codes is the simulation of electrostatic waves.