O/R Sector heavyweight Beach Energy BPT.AX rose 4.1%, leading gains on the sub-index, while Woodside Petroleum WPL.AX advanced nearly 2%. By Navya Mittal April 19 (Reuters) - Australian shares rose on Tuesday to a 3-1/2-month closing high, lifted by gains in miners and energy firms on strong underlying commodity prices, while rising inflation was seen nudging the central bank to move closer towards hiking interest rates. Miners .AXMM advanced 1.2% to lead gains on the benchmark after iron ore futures jumped overnight on hopes of additional stimulus to support China's economy.