MHD modeling of the Heliosphere: a critical evaluation of different models

International audienceThe very complicated problem of the solar wind-interstellar medium interaction requires a very sophisticated numerical approach. To achieve such a goal first we need to understand very deeply the results obtained up-to-now. In this paper we gather the results from four different MHD models of the heliospheric interfaces. The comparison of the results invokes several questions. These questions should be addressed before we proceed with the next steps in the MHD modeling of the heliospheric interfaces. Is a jet created between the termination shock and the heliopause (Opher et al., 2003, 2004)? What is the physical meaning of the V-shape of termination shock and heliopause (Washimi and Tanaka, 2001, 2004)? Whether a similar looking result is either due to bending of the heliospheric current sheet as in the model by Pogorelov (2004), Pogorelov et al. (2004) or due to numerical "reconnection" as in the model by Ratkiewicz et al. (2004, 2005)? The purpose of this paper is to open a wider discussion to try to answer these questions