Adaptive Osher-type scheme for the Euler equations with highly nonlinear equations of state

摘要: Abstract For the numerical simulation of detonation condensed phase explosives, a complex equation state (EOS), such as Jones–Wilkins–Lee (JWL) EOS or Cochran–Chan (C–C) EOS, are widely used. However, when conservative scheme is used for solving Euler equations with state, spurious solution across contact discontinuity, well known phenomenon in multi-fluid systems, arises even single materials. In this work, we develop generalised Osher-type an adaptive primitive–conservative framework to overcome aforementioned difficulties. Resulting solutions compared exact and from Godunov method conjunction Riemann solver Mie–Gruneisen form JWL C–C state. The extended second order its empirical convergence rates presented, verifying accuracy smooth solutions. Through suite several tests problems one two space dimensions illustrate failure schemes capability methods paper