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We develop a new heavy quark transport model, QLBT, to simulate the dynamical propagation of heavy quarks inside the quark-gluon plasma (QGP) created in relativistic heavy-ion collisions. Our QLBT model is based on the linear Boltzmann transport (LBT) model with the ideal QGP replaced by a collection of quasi-particles to account for the non-perturbative interactions among quarks and gluons of the hot QGP. The thermal masses of quasi-particles are fitted to the equation of state from lattice QCD simulations using the Bayesian statistical analysis method. Combining QLBT with our advanced hybrid fragmentation-coalescence hadronization approach, we calculate the nuclear modification factor$$R_\mathrm {AA}$$$R_{\mathrm{AA}}$and the elliptic flow$$v_2$$$v_2$ofDmesons at the Relativistic Heavy-Ion Collider and the Large Hadron Collider. By comparing our QLBT calculation to the experimental data on theDmeson$$R_\mathrm {AA}$$$R_{\mathrm{AA}}$and$$v_2$$$v_2$, we extract the heavy quark transport parameter$$\hat{q}$$$\hat{q}$and diffusion coefficient$$D_\mathrm {s}$$$D_s$in the temperature range of$$1-4~T_\mathrm {c}$$$1-4T_c$, and compare them with the lattice QCD results and other phenomenological studies.