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Table 3 Two 1-D Riemann problems for compressible inviscid flow

From: High-order compact gas-kinetic schemes for three-dimensional flow simulations on tetrahedral mesh

Test cases

\(\rho _L\)

\(U_L\)

\(p_L\)

\(\rho _R\)

\(U_R\)

\(p_R\)

\(x_D\)

\(t_f\)

Lax shock tube problem

0.445

0.698

3.528

0.5

0

0.571

0.5

0.16

Large pressure ratio problem

\(1\times 10^4\)

0

\(1\times 10^4\)

1

0

1

0.3

0.12