Conservative front tracking and level set algorithms

Conservative front tracking and level set algorithms.

Hyperbolic conservation laws are foundational for many branches of continuum physics. Discontinuities in the solutions of these partial differential equations are widely recognized as a primary difficulty for numerical simulation, especially for thermal and shear discontinuities and fluid-fluid internal boundaries. We propose numerical algorithms that will (i) track these discontinuities as sha...

Conservative Front Tracking in Higher Space Dimensions

We propose a fully conservative Front Tracking algorithm in two space dimension. The algorithm rst uses the point shifted algorithm 12] on two adjacent time levels and then constructs space time hexahedra as computational units. We develope and prove a successful geometric construction under certain interface requirement. This algorithm has a rst order local truncation error for cells near the ...

Conservative Front Tracking with Improved Accuracy

We propose a fully conservative front tracking algorithm for systems of nonlinear conservation laws. The algorithm improves by one order in its convergence rate over most finite difference schemes. Near tracked discontinuities in the solution, the proposed algorithm has O(∆x) errors, improving over O(1) errors commonly found near a discontinuity. Numerical experiments which confirm these assert...

A Conservative Front Tracking Method in N -Dimensions

We propose a fully conservative Front Tracking algorithm for systems of nonlinear conservation laws. The algorithm can be applied uniformly in one, two, three and N dimensions. Implementation details for this algorithm and tests of fully conservative simulations are reported.

A Conservative Front Tracking Method for Hyperbolic Conservation Laws