
türmen
to flee
Colloquial for to flee or run away, often in order to escape an unpleasant situation or punishment.
Als die Polizei kam, ist der Dieb sofort getürmt.
When the police came, the thief fled immediately.
to flee / to pile up
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to flee
Colloquial for to flee or run away, often in order to escape an unpleasant situation or punishment.
Als die Polizei kam, ist der Dieb sofort getürmt.
When the police came, the thief fled immediately.

to pile up
To accumulate into a great height or quantity. Often used for clouds, problems, or objects.
Die dunklen Gewitterwolken türmten sich am Horizont.
The dark storm clouds piled up on the horizon.

to stack up
To stack something into a tower or a high pile.
Die Kinder türmten die Bauklötze zu einem hohen Turm.
The children stacked the building blocks into a tall tower.
The verb 'türmen' (to pile up/to flee) is derived from the noun 'der Turm' (tower). The meaning 'to stack something up' is the most literal one. The reflexive form 'sich türmen' describes how something accumulates to a tower-like height.
Die Kinder türmen die Kissen auf dem Sofa.
The children pile up the cushions on the sofa.
The three meanings can be distinguished well grammatically. The colloquial meaning 'fliehen' (to flee) is intransitive. The meaning 'sich anhäufen' (to accumulate) is reflexive ('sich türmen'). The meaning 'aufstapeln' (to stack up) is transitive and needs an accusative object.
Der Einbrecher ist sofort getürmt.
The burglar fled immediately.
In the meaning 'fliehen' (to flee), 'türmen' is a verb of motion. Therefore, the perfect tense is formed with the auxiliary verb 'sein' (to be), not with 'haben' (to have).
Als er das Martinshorn hörte, ist er sofort getürmt.
When he heard the siren, he fled immediately.
Using 'türmen' to mean 'fliehen' (to flee) is clearly colloquial. In formal or written contexts, you would use other verbs.
Kaum hatte ich ihn zur Rede gestellt, ist er getürmt.
No sooner had I confronted him than he took off.
The reflexive form 'sich türmen' (to pile up) is often used for things that accumulate. Typical examples are 'die Arbeit' (work), 'die Schulden' (debts), 'die Probleme' (problems), or 'die Wolken' (clouds).
Am Horizont türmten sich bereits die Gewitterwolken.
Storm clouds were already piling up on the horizon.
to flee
Fliehen and türmen can both express that someone leaves because they are afraid of danger or punishment. Fliehen is the neutral, more serious word, while türmen sounds colloquial and often presents the quick escape more casually. Fliehen fits an official report, whereas türmen is more natural in a conversation among friends.

Der Junge türmte, als er die Polizei vor dem Haus sah.
The boy took off when he saw the police outside the house.
Der Mann floh aus Angst vor der drohenden Strafe.
The man fled because he was afraid of the impending punishment.