AN ANALYTICAL TEST FOR GAS DYNAMICS SIMULATIONS WITH NONLINEAR HEAT CONDUCTION
В. P. Tikhomirov
VANT. Ser.: Mat. Mod. Fiz. Proc 2008. Вып.4. С. 31-36.
A problem of discontinuous running waves propagating in cold matter at a constant velocity is considered for ID gas dynamics equations in Lagrange variables. As an equation of state we use the EOS of ideal gas without energy and pressure of equilibrium radiation and with it. The heat conduction coefficient is chosen in a special way: in the form of a product of an arbitrary power function of temperature and some well-defined density and temperature-dependent function. As a result, self-similar equations of the running wave problem become much simpler and easier to integrate. The resulting exact solution has a simple analytical representation. For still gas, it agrees with the well-known solution to the heat wave problem. The exact solution thus obtained can be used as a benchmark for codes and numerical solvers of gas dynamics equations with non-linear heat conduction. The analytical solution is compared with a solution obtained by the difference technique.
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