Abstract
We present a user-friendly and intuitive C++ expression system to implement numerical simulations of continuum biological hydrodynamics. The expression system allows writing simulation programs in near-mathematical notation and makes codes more readable, more compact, and less error-prone. It also cleanly separates the implementation of the partial differential equation model from the implementation of the numerical methods used to discretize it. This allows changing either of them with minimal changes to the source code. The presented expression system is implemented in the high-performance computing platform OpenFPM, supporting simulations that transparently parallelize on multi-processor computer systems. We demonstrate that our expression system makes it easier to write scalable codes for simulating biological hydrodynamics in space and time. We showcase the present framework in numerical simulations of active polar fluids, as well as in classic simulations of fluid dynamics from the incompressible Navier–Stokes equations to Stokes flow in a ball. The presented expression system accelerates scalable simulations of spatio-temporal models that encode the physics and material properties of tissues in order to algorithmically study morphogenesis.Graphicabstract
Highlights
Numerical simulations of mathematical models of biological processes in space and time have become an integral part of studying the physical principles of living systems [1]
Coupling biological hydrodynamics with biochemical regulation, such models have been successful at describing the physics underlying biological phenomena such as cell division [5], zygote polarization [6,7], epithelial tissue folding [8], and cellular symmetry breaking [9]
Simulation software implementations are typically specific to a certain numerical method and a certain partial differential equations (PDE) model, with discretized differential operators hard-coded in explicit program statements
Summary
Numerical simulations of mathematical models of biological processes in space and time have become an integral part of studying the physical principles of living systems [1]. For example to test new hypotheses, usually requires rewriting much of the simulation program This is time-consuming, and creates challenges in terms of code structure and maintainability, as well as computational speed and parallel scalability. There is a need for generic simulation software platforms that separate the PDE model to be simulated from the numerical methods and that accelerate the implementation of efficiently scalable parallel computer programs. We present such a generic simulation environment based on the OpenFPM parallel computing framework [16]. We show how our framework allows to change the numerical method by providing examples using both grid-based finite-difference methods and mesh-free particle methods
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