  We study the initiation of thermonuclear detonations in tidally disrupted
white dwarf stars by intermediate-mass ($10^3 M_\odot$) black holes. The length
scales required to resolve the initiation mechanism are not easily reached in
three-dimensions, so instead we have devised two-dimensional proxy models
which, together with a logarithmic gridding strategy, can adequately capture
detonation wave fronts as material undergoes simultaneous compression and
stretching from tidal forces. We consider 0.15 and 0.6 solar mass white dwarf
stars parameterized by tidal strengths in the range $\beta=4~\text{to}~23$.
High spatial resolution elucidates the manner and conditions leading to
thermonuclear detonation, linking the initiation sequence to stellar
composition and tidal strength. All of our models suffer sustained detonations
triggered by a combination of adiabatic compression, mild thermonuclear
preconditioning, and collisional heating, in degrees depending primarily on
tidal strength. We find many diagnostics, such as temperature, total released
energy, and iron group products, are fairly well-converged (better than 10%) at
resolutions below 10 km along the scale height of the orbital plane. The
exceptions are intermediate mass transients like calcium, which remain
uncertain up to factors of two even at 1 km resolution.
