Simulation movies of tumor growth under Darcy’s law with heterogeneous conductivity

Introduction: this page lists some movies produced from numerical simulation attached to the paper Xiaoming Zheng , Kun Zhao, Trachette Jackson, John Lowengrub. Tumor growth towards lower extracellular matrix conductivity regions under Darcy’s Law and steady morphology. Journal of Mathematical Biology, 85, Article number 5 (2022)

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For the simulation presented in the paper, we have 3 videos here. Note the conductivity is assumed to be K(x,y)=exp(4x+2y). We observe that the tumor grows to the negative gradient direction of this conductivity field, that is, (-4, -2) direction.

Movie 1: surface tension tau=0, that is, no surface tension. In this case, the growth is very unstable.

Movie 2: the surface tension coefficient tau=0.05

Movie 3: the surface tension coefficient tau=8.