Computation of normal shocks running into a cloud of particles using a high-order particle-source-in-cell method.

In this paper, the two-dimensional particle-laden flow developments are studied with bronze particle cloud in the accelerated flow behind a running shock. The forty thousands particle clouds are arranged initially in a rectangular, triangular and circular shape. The flows are computed with a recently developed high-order Eulerian-Lagrangian method, that approximates the Euler equations governing the gas dynamics with the improved high order weighted essentially non-oscillatory (WENO-Z) scheme, while individual particles are traced in the Lagrangian frame using high-order time integration schemes. A high-order ENO interpolation determines the carrier phase properties at the particle location. A high-order central weighing deposits the particle influence on the carrier phase. Reflected shocks form ahead of all the cloud shapes. The detached shock in front of the triangular cloud is weakest. At later times the wake behind the cloud becomes unstable and a two-dimensional vortex-dominated wake forms. Separated shear layers at the edges of the clouds pulls particles initially out of the clouds that are consequently transported along the shear layers. Since flows separated trivially at sharp corners, particles are mostly transported out of the cloud into the flow at the sharp front corner of the rectangular cloud, and the trailing corner of the triangular cloud. Particles are transported smoothly out of the circular cloud, since it lacks sharp corners. At late times, the accelerated flow behind the running shock disperses the particles in cross-stream direction the most for the circular cloud, followed by the rectangular cloud and the triangular cloud.