The current paper presents the numerical simulation of the wave propagation phenomena in the Newtonian and non-Newtonian drilling mud flow associated with oil/gas drilling activities. The formation of wave due to back pressure changes by means of a choke is investigated. Numerical schemes with second- and forth-order accuracy have been applied to the non-linear Euler and Navier-Stokes equations to demonstrate the advantage of high-order approximation in numerical modeling. A grid refinement study is performed to observe the convergence of the solution with respect to various time steps and grid sizes. Conservative and non-conservative formulations of momentum equations were explored to evaluate the accuracy of reflection and transmission of pressure pulse at the areal discontinuity in the conduit.

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