Adaptive Level-set Methods For Numerical Integrations On Arbitrary Interfaces And Arbitrary Domains

In this work, we study numerical integration over arbitrary interface and arbitrary domain by using the block-structured adaptive mesh. The arbitrary interface and arbitrary domain are described by a level set func-tion. We first describe the numerical methods in the literature for the integrations on uniform Cartesian grid. Then we extend the methods to the block-structured adaptive mesh. Numerical calculations demonstrate that the adaptive mesh methods are second-order accurate. Compared to the uniform mesh methods, the adaptive mesh methods reduce the needs of computer storage significantly.