An explicit integration algorithm for computations of wave propagation in solids is presented, which is designed to trace extensional and shear waves in accordance with their respective propagation speeds. This has been possible by an orthogonal decomposition of the total displacement into extensional and shear components. The two decoupled wave equations are integrated with a newly developed algorithm[1, 2] that is proven to be effective in mitigating spurious oscillations. The essence of the present algorithm consists of a combination of two wave capturing characteristics: a new integration formula that is designed to filter post-shock oscillations and the central difference method that is known to intrinsically filter out front-shock oscillations. A judicious combination of these two wave capturing characteristics is shown to reduce substantially both spurious front-shock and post-shock oscillations. Numerical experiments have demonstrated that the present algorithm traces the stress wave fronts with high-fidelity for both linear and nonlinear wave propagation problems.

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