A fully explicit gas-liquid two-phase flow solver based on weakly compressible assumption with interface-adapted AMR method is proposed to avoid solving pressure Poisson equation for large-scale two-phase flow simulations. We evaluate isothermal Navier-Stokes equation which can help to give us the speed of sound as a constant parameter in whole computational domain. The conservative Allen-Cahn equation, which is one of the phase-field models, is solved by finite volume method with continuum equation. The AMR method greatly reduces the computational cost by assigning high-resolution mesh to the region around the moving gas-liquid interface. We have developed the GPU-code of the tree-based AMR on staggered grid system and the allocation, deallocation and defragmentation of device memory are performed in own code to improve computational efficiency. Several benchmark problems are examined and the results of weakly compressible scheme based on isothermal Navier-Stokes equation are in good agreement with the experimental and computational references. We successfully applied the density-weighted advection evaluation to our weakly compressible solver in order to improve the evaluation of momentum effect near the gas-liquid interface caused by velocity-based solver. The behavior of rising bubble colliding the liquid interface were simulated by using our method, the thin liquid film can be reproduced by using $9.765 \times 10^{-3}\ \mathrm{mm}$ mesh with 8-level refinement for the interface to 10mm computational domain.
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