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Density waves excited by planets embedded in protoplanetary disks play acentral role in planetary migration and gap opening processes. We carry out 2Dshearing sheet simulations to study the linear regime of wave evolution withthe grid-based code Athena, and provide detailed comparisons with thetheoretical predictions. Low mass planets (down to ~0.03 Earth mass at 1 AU)and high spatial resolution (256 grid points per scale height) are chosen tomitigate the effects of wave nonlinearity. To complement the existing numericalstudies, we focus on the primary physical variables such as the spatial profileof the wave, torque density, and the angular momentum flux carried by the wave,instead of secondary quantities such as the planetary migration rate. Ourresults show percent level agreement with theory in both physical and Fourierspace. New phenomena such as the change of the toque density sign far from theplanet are discovered and discussed. Also, we explore the effect of thenumerical algorithms, and find that a high order of accuracy, high resolution,and an accurate planetary potential are crucial to achieve good agreement withthe theory. We find that the use of a too large time-step without properlyresolving the dynamical time scale around the planet produces incorrectresults, and may lead to spurious gap opening. Global simulations of planetmigration and gap opening violating this requirement may be affected byspurious effects resulting in e.g. the incorrect planetary migration rate andgap opening mass.

Density Waves Excited by Low-Mass Planets in Protoplanetary Disks I: Linear Regime