Semi-analytical implicit direct time integration method for 1-D gas dynamic problem

Sharp wave treatment for 1-D gas dynamic problem is still a chellenge modern numerical methods. They often require too many space and time steps, produce spurious oscillation of solution, exhibit strong dissipation or divergence results. This paper further extension authors’ idea employment the analytical solution coordinate, where step parameter which used in solution. Its peculiarity consists development additional procedure linearization dependence between pressure density. It performed premise that actual each element close to basic pressure, attained at previous moment time. The efficiency method tested on very popular task Sod, two different ideal gases tube are separated by diaphragm, suddenly broken. considered Lagrangian coordinates formulation. results obtained show good method, requires essentially lesser leads no give consistent predictable with respect meshing. accuracy mostly controlled step, should be larger than clearly stated theoretical lower limit. Other advantage it can calculate process any desired time, meshing variable easily adapted during calculation.